Straight lines Questions and Answers

A ferry takes several trips between points A and B. It moves at a constant speed of 0.35 miles/minute and takes the same route on each trip. Thetotal duration of a round trip from point A to point B and back is 80 minutes, ignoring the time spent stopped at point B. If d is the ferry's distance from point A in miles and t is the time in minutes, which equation models the ferry's distance from point A for the duration of the trip? d=-10.35r-40| +40 d=-10.35-80| +80 . d=-10.35r-281 +28 . d=-10.35-141 +14

Suppose the line of best fit for some data points has a slope of 4.404. If the mean of the x-coordinates of the data points is 8.891, and the mean of the y-coordinates is 5.519, what is the y-intercept of the line to three decimal places? A. 15.415 B. -15.415 C. 33.637 D. -33.637

If you have 140 meters of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose? Area = (include units)

Given f(x) = 4x - 3x² and m(x) = 4 - 6x: a) Write the equation of the tangent line to f(x) when x = 0. b) Write the equation of the tangent line to f(x) when x = 2. c) At what ordered pair does f(x) have a tangent slope of 16 ?

Given f(x) =2x+6/ 4x+8 and m(x) = -1/2(x+2)² a) At what ordered pair is the tangent line horizontal? (clue: a horizontal line has a slope of zero) b) At what ordered pairs does the normal line have a slope of 32 ? c) What is the slope of the normal line when y=0?

Prove that the polygon with coordinates A(5, 6), B(8, 5), and C(2, -3) is a right triangle. a) slope of CB 4/3 =;slope of AC = 3; perpendicular lines form a right angle b) slope of AB=1/3 ;slope of CB =4/3 both have denominators of 3 making the perpendicular c) cannot be proven d) slope of AB =-1/3 slope of AC = 3; perpendicular lines form a right

How can coordinate proof be used to prove two lines are parallel? a) Show that the product of their slopes is 1. b) Show that the product of their slopes is -1. c) Show that the slopes are the same. d) Show that the y-intercepts are the same.

Give the slope and y-intercept for the following equation. 2r + 5y = 10

Find the equation of the line containing the point whose coordinates are (-1, 2) and perpendicular to the graph of 3x + 9y = -3.

A line is parallel to the x-axis and passes through (2, 3). Which answer choice shows the line's equation and correct slope? x = 3; m = 0 y = 2; m = undefined x = 2; m = undefined y = 3; m = 0

Which of the following equations represents a line that passes through the points (-6, 10) and (-8, 16)? I. 3x + y = -8 II. y=-3x -7 Neither II only I only I and II

Find equations of the lines that pass through the given point and are parallel to and perpendicular to the given line. 4x - 2y = 7, (2, 1) (a) parallel to the given line (b) perpendicular to the given line

Which line is parallel to the line y = −4x+6 and passes through the point (-2, 5)? Write your answer as y=mx+b with no spaces. Use parenthesis if your slope is a fraction. For example, if your answer is y = −3x/4+1, you would type your answer as y=(-3/4)x+1

Which line is perpendicular to the line y = 1/5 x - 1 and passes through the point (-2,-4)? Write your answer as y=mx+b with no spaces. Use parenthesis if your slope is a fraction. For example, if your answer is y=-3/4x+1. you would type your answer as y=(-3/4)x+1 -

Which classification describes the following system of equations? 5x+y+2z-13 4x+3y+6z=17 x+2y=4 inconsistent and dependent consistent and dependent consistent and independent inconsistent and independent

Which line is perpendicular to the line y = −1/2 x - 5 and passes through the point (-3, 2)? Write your answer as y=mx+b with no spaces. Use parenthesis if your slope is a fraction. For example, if your answer is y = − 3/4 x + 1, you would type your answer as y=(-3/4)x+1

Identify if the system of linear equations is parallel, perpendicular, coincident, or intersecting but, not perpendicular (IBNP). y = -3x = −3x − 2 Coincident Parallel IBNP Perpendicular

Which line is perpendicular to the line y = x + 5 and passes through the point (-7, 2)? Write your answer as y=mx+b with no spaces. Use parenthesis if your slope is a fraction. For example, if your answer is y = -3/4 x + 1. you would type your answer as y=(-3/4)x+1

Which line is parallel to the line y = 1/2x– 10 and passes through the point (8, -7)? Write your answer as y=mx+b with no spaces. Use parenthesis if your slope is a fraction. For example, if your answer is y = -3/4x + 1. you would type your answer as y=(-3/4)x+1

The equations of three lines are given below. Line 1: 10x-4y=-6 Line 2: y=-2/5x+8 Line 3: 5y=-2x+6 For each pair of lines, determine whether they are parallel, perpendicula Line 1 and Line 2: Parallel Perpendicular Neither Line 1 and Line 3: Parallel Perpendicular Neither Line 2 and Line 3: Parallel Perpendicular Neither

Consider the curve y = 5x3 - 3x. (a) Find dy/dx. The curve has a tangent at the point P(-1.-2). (b) Find the gradient of this tangent at point P. (c)Find the equation of this tangent. Give your answer in the form y = mx + c.

The rectangular coordinates of a point are given. Find polar coordinates (r,0) of this point with 8 expressed in radians. Let r>0 and -2л<0<2л. (-10,10) One possibility for the polar coordinates of this point is. (Simplify your answer. Type an ordered pair. Type your answer in radians. Type exact answers, using as needed. Use integers or fractions for any numbers in the expression.)

The senior classes at High School A and High School B planned separate trips to the indoor climbing gym. The senior class at High School A rented and filled 12 vans and 9 buses with 435 students. High School B rented and filled 5 vans and 3 buses with 155 students. Every van had the same number of students in it as did the buses. How many students can a van carry? How many students can a bus carry?

If you drive 165 miles and have 15 gallons of gas remaining in your tank. Then you continue driving, and calculate that after driving 298 miles you have 8 gallons left. What is your rate?

The equation of the line L₁ is 2x + y = 10. Write down (i) the gradient of L₁; (ii) the y-intercept of L₁. 1b. [2 marks] The line L, is parallel to L, and passes through the point P(0, 3). Write down the equation of L₂. 1c. [2 marks] The line L, is parallel to L, and passes through the point P(0, 3). Find the x-coordinate of the point where L₂ crosses the x-axis.

If g(x) is the ƒ(x) = x after a vertical compression by 2/5 a shift right by 4, and a shift down by 2, a) write an equation for g(x): g(x) = b) The slope of this line is: c) The vertical intercept of this line is:

Find an equation of the line that passes through the given point and has the indicated slope m. Point (-2,-5) Slope m= 4/5

The equation for line t can be written as y = -4x + 8. Perpendicular to line t is line u, which passes through the point (-8, -8). What is the equation of line u? Write the equation in slope-intercept form. Write the numbers in the equation as proper fractions, improper fractions, or integers.

Stephen opens a savings account with an initial deposit of $300. Every month, Stephen will deposit an additional $250 into the account from his paycheck. Which function below shows the total amount of his deposits for x number of months? y=12x+550 y=x(300+250) y = 250x + 300 y = 300x + 250

WHAT IS THE EQUATION OF THE LINE THAT PASSES THROUGH THE POINT (4.4) AND HAS A SLOPE OF 1/47 Show your work below and put your answer in the blue box. Use point-slope form to start.

What is the equation of a line with a y-intercept of -3 and a slope of -4/5? -4x+ 5y = 15 4x + 5y = -15 -4x + 5y = -3 4x + 5y = 3

Does a system of linear equations always have a solution? What about the following system? x + 3y = 1; 2x+6y=3 If we think of the two equations in the above system as two "straight lines" in the plane, can you explain why the system doesn't have a solution?

Which statement is true regarding the line y = -4x + 13? The line has a slope of -13. The line has a slope of 4. The line passes through the point (0, 13). The line passes through the point (0, - 4).

A system of equations is shown below. 3x - 2y = 7 9z - 6y = k What statement is true about the relationship between the value of k and the number of solutions for the system of equations? For any value of k, the system of equations has no solution. For any value of k, the system of equations has infinitely many solutions. If k is equal to any value other than 21, the system of equations has no solution. If k is equal to any value other than 21, the system of equations has infinitely many solutions.

Your school is printing programs for the honor society induction ceremony. L & L Printing will print the programs for $350 plus an additional $1.50 per program. Red Baron will print the programs for $1.82. Identify the y-intercept for each of the Printing Companies. L & L Printing = Red Baron =

Compute the slope (constant rate of change) of the line connecting the points. (-10, 21) and (20,-24). If the slope is undefined, enter N/A in the blank. The slope (constant rate of change) is

Ms. Scott will pay $2,000 to have her house painted. The amount each painter earns, A, varies inversely for the number of painters, n, that will paint the house. Which equation best represents this situation?

Find the equation in x and y for the line tangent to the curve given parametrically by x = sint, y = cost, at the point on the curve associated with t=π/4 y =

The point P(2, -1) lies on the curve y = 1/(1-x). (a) If Q is the point (x, 1/(1-x)), use your calculator to find the slope of the secant line PQ (correct to six decimal places) for the following values of x: (ii) 1.9 (iii) 1.99 (vi) 2.1 (vii) 2.01 (i) 1.5 (v) 2.5 (iv) 1.999 (viii) 2.001 (b) Using the results of part (a), guess the value of the slope of the tangent line to the curve at P(2, -1). (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(2, -1).

The line y = x makes a 45° angle with the y-axis. What angle does the line y = x + 5 make with the y-axis? What angle would the line y = x + 5 make with any vertical line? Justify your answer.

Graph the system below and write its solution. 3x+y=-3 y=-1/2x+2

Graph the linear equation by finding and plotting intercepts. y = 3x

Consider the following absolute value inequality. |9x + 7| < 10 Determine which graph represents the original inequality.

Let f (x) = 5x - 2. Describe the transformations from the graph of f to the graphs of g(x) = f(x - 5) and h(x) = f(x) +2. The graph of g is a of the graph of f. The graph of h is a of the graph of f.

Line A has a slope of -2/5 and passes through the point (2, 6). Line B has a slope of 1/3 and passes through the point (-33, -2). Find the point where line A intersects line B. A. x = -1, y = 8² B. I = -3, y = 8 C. I = 8, y = -3 D. I = 17, y = 0

The equation of line A is y= 7x + 14. Line B is perpendicular to line A and passes through the point (4, 13 3/77). What would be the solution to the system of equations represented by line A and line B? A. The system of equations has no real solutions. B. x = 14, y = 0 C. x = 0, y = 14 D. The system of equations has an infinite number of real solutions.

A drill is used to dig down into the earth. After 2 hours, the drill is 12 meters below. the surface. After 5 hours, the drill is 30 meters below the surface. Which equation represents the depth of the drill in meters, y, after x hours of drilling?

Use the following system of equations to answer the following: ax + 5y = 2 3x+10y = 4 a. Write both equations in slope-intercept form. (You must show work in order to receive full credit.)

Find the coordinates of both intercepts for the line. Express numbers in exact simplified form. -8x-3y=-23 The X intercept has the coordinates The intercept has the coordinates

Given g(x)=x²-4x, find the equation of the secant line passing through (-4, g (-4)) and (2, g (2)). Write your answer in the form y=mx+b.