Straight lines Questions and Answers

Graph the line that passes through the points (-5, 2) and (6, 2) and determine the equation of the line.

Graph the line with the equation y = -1/2x – 6.

Graph the line with the equation y =1/6 x - 5.

What is the slope of the line that passes through the points (1, -6) and (-8, 9)? Write your answer in simplest form.

The line L₁ passes through the point P(-5,-3) and it is tangent to the graph of y = (x+3)2-7. The line L2 is parallel to L₁ and it is tangent to the graph of y = 5-(x - 1)². Find the y-intercept of L2.

Write the point slope form of the equation of a line parallel to y = -x + 3that passes through the point (-5, 3). Oy - 3 = (x + 5) Oy-3= -(x - 5) Oy+ 3 = ²(x + 5) Oy=-x-1 Oy - 3 = (x + 5) -

For which point (x,y) is the slope of the line between (8,8) and (x,y) equal to the slope of the line between (8,8) and (-3,5). (Use the interactive figure to find your answer.) Click here to launch the interactive figure. Choose the correct answer below. O A. (11,19) B. (8,8) C. (0,0) D. (19,11) *****

If algebraic sum of lengths of perpendiculars drawn from vertices of a hexagon ABCDEF, A(-2,-1), B(0,-2), C(4,0), D(3,2), E(2,3), F(-1,4) on a variable line ax + by + c = 0 is zero, then variable line always passes through a fixed point (p,q), then the value of p + q is

Write the standard form of the equation of the line through the given points. through: (3,-2) and (-1,-5) A) 3x-4y=-16 B) 3x - 4y = 17 C) 3x+4y= 16 D) 3x - 4y = 16

Given the equation: y - 3 = 4(x+2) Find The slope of a line parallel to the line above The slope of a line perpendicular to the line above

Given the Points J(-8, -2) and K(4,2) Find The slope of a line that is parallel to line JK The slope of a line that is perpendicular to line KJ

What is the slope of the line with the equation x = 3? 3 Undefined 0

When Emmy went to bed, it was a frigid 9°F outside. The temperature has been dropping 2°F each hour. Write an equation that shows the relationship between the number of hours since Emmy went to bed, x, and the temperature in °F, y. y =

Write the slope-intercept equation of the function f whose graph satisifies the given conditions. The graph of f passes through (-12,6) and is perpendicular to the line that has an x-intercept of 1 and a y-intercept of - 3. The equation of the function is. (Use integers or fractions for any numbers in the equation.)

What is the equation, in point-slope form, for a line that goes through (8,-4) and has a slope of -5/6? y-4=-5/6 (x-8) y+4=-5/6 (x-8) y+4= -5/5(x+8) y-4 =-5/6(x+8)

Sometimes linear equations are written in forms other than y C ma+b. One common form looks like Ar+By C. When you see an equation like this, you can find the slope and y-intercept by solving the equation for y, rewriting it into slope-intercept form. Rewrite 5x y = 15 into slope-intercept form by solving for y. y From that we can see that: m= = b. =

Micah invests $6800 in two different accounts. The first account paid 8 %, the second account paid 2 % in interest. At the end of the first year he had earned $406 in interest. How much was in each account? S $ at 8 % at 2%

Rigid Transformations:Question 8 Triangle MNO has points M = (-6,-1), N= (-3,- 7), and O= (-1,-1). Triangle M'N'O' has points M = (6,1), N'=(3,7), O = (1,1). What is the transformation of MNO to M'N'O'? one: O O O Reflected about the y-axis and then translated up 2 Reflected about the x-axis and then shifted to the right 12 Rotation of 270 degrees counterclockwise Reflected about the y-axis and then reflected about the x-axis

Which of the following is an equation of the line tangent to the graph of x2-3xy = 10 at the point (1, -3)? (A) y + 3 =-11 (x-1) (B) y + 3 = -7/3 (x-1) (C) y + 3 = 1/3 (x-1) (D) y + 3 = 7/3 (x-1) (E) y + 3 = 11/3 (x-1)

Graph the line with slope -2 passing through the point (4, -4).

Consider the curve given by the parametric equations x = sint, y = sin(t + sin t) where -∞ < t < c. Note that it has two tangents at the origin (0,0) since both t = 0 and t = π corresond to the origin. Find the equations of the two tangents to the curve at the origin.

Graph the line with slope -1 passing through the point (-3,2).

Graph the line with slope 1/2 and y-intercept 4.

Determine the slope of the line that contains the given points. 1. S(-1, 2). W(0, 4) 2. G(-2,5), H(1,-7) 3. C(0, 1), D(3, 3) 4. J(-5,-2), K(5,-4)

Use technology to find points and graph the line 6y= 2x - 12, followin the instructions below. Plot at least two points that fit on the axes below. Click a point to delete it.

Gabriel is signing up for a gym membership with a one-time fee to join and then a monthly fee to remain a member. The monthly fee is $40 and the one-time joining fee is $100. Write an equation for C, in terms of t, representing the total cost of the gym membership over t months.

Suppose a vine maple grows in height linearly. Four weeks after it is planted it stands 7.8 inches, and after nine weeks it is 13.8 inches tall. Write an equation that models the growth, in inches, of the vine maple as a function of time, in weeks. 1) What is the slope of the function? 2) How tall was the tree when it was first planted? 3) Write the function 4) How tall will the vine maple be after 16 weeks?

Find the slope of the line passing through the points (3, 8) and (7,-7).

Jessica is making a map of her school on a coordinate plane. Two hallways in the school are perpendicular to each other. The main hallway passes through the points (-5, 9) and (4, 6). The perpendicular hallway passes through the point (-4, 3). Part A Find the equation for the line that represents the main hallway.

What's the equation of the line that's a perpendicular bisector of the segment connecting A (-2, 8) and B(-4, 2)? OA) y = -1/3x - 3 OB) y = -1/3x + 3 OC) y = ¹/3x + 3 OD) y = -¹/3x+4

2. at a trail head and hike into the forest to a campsite. The next morning, they head out on a hike from their campsite walking at a steady rate. The graph shows their distance in miles, d, from the car on the day of their hike after h hours. dA How far is the campsite from their car? Explain how you know. b. Write an equation that describes the relationship between d and h. C. After how many hours will the hikers be 16 miles from their car? Explain or show your reasoning. 15 10 5

The equation of line c is y = 5x - 2/5. Line d is parallel to line c and passes through (2, 6). What is the equation of line d? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Find the point on the line 3x + y + 4 = 0 which is closest to the point (1, 4).

The equation of line t is y = -1/8x - 8. Line u is parallel to line t and passes through (8, 5). What is the equation of line u? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

The graph of an exponential function has a y-intercept of 7 and contains the point (4, 112). Construct the exponential function that describes the graph. Provide your answer below: f(x)=

Solve each system by substitution. -8x - 5y = 7 4x + 4y = 4 Infinite number of solutions (-4,5) (5,-3) (-7,-3) (-5,-4)

Find the x-intercept of the following line. Enter an ordered pair. Y = 9 x-1

Graph the linear equation. Find three points that solve the equation, then plot on the graph. -x-2y = 8

What are the slopes and y-intercepts of the lines having the following equations? (If necessary, first write the equation in slope- intercept form.) a) y = 8x + 3 b) y = 1/2x + 5 c) y = x - 7 d) y = 6(x - 2) e) y = x + x f) y = -x g) y = 10 - 3x h) y = 4

Pete estimates that he has spent $64.50 on supplies for his lawn mower. He charges $12 per lawn for his service. Write a linear model in the form y = mx + b where y represents the amount of profit Pete earns for mowing a number of lawns.

A cellular service provider charged a customer $40 for 150 minutes of airtime. The same provider charged another customer $55 for 300 minutes of airtime. What linear model represents the total cost, C, as a function of t, the amount of airtime in minutes?

Find the equation of the line through (8, -7) which is perpendicular to the line y = x/2 = -9. Give your answer in the form y = mx + b.

Rewrite the linear function 5x + 1/3y= -2 in slope-intercept form. re: O y=-15-2 O g=-15-6 O O 5 2-2 2 3

Find the x- and y-intercept of the line. -10 + 5y = 40 x-intercept is 5; y-intercept is negative 10 x-intercept is 8; y-intercept is negative 4 x-intercept is negative 10; y-intercept is 5 x-intercept is negative 4; y-intercept is 8

A line has a slope of -6 and includes the points (h, -3) and (-6, -9). What is the value of h? h =

Mike created a shoe store named "Be like Mike Shoe Store." Mike offers a frequent-buyers card. Each transaction is worth 8 points, and customers automatically earn 20 points when they sign up. a) Write an equation for the function that gives the card value based on the number of transactions that have occurred. b) What is the y-intercept for this linear function, and what does it represent? c) What is the slope for this linear function, and what does it represent? d) For each 260 points, the customer receives a gift certificate. How many transactions will it take for the customer to earn the first gift certificate? 7

Write an equation in y = mx + b form for the linear relationship shown in the table. X Y -2 1 1 13 3 21 4 25 8 41

Point I is on line segment HJ. Given HI = x, HJ = 3x -9, and IJ = x + 5, determine the numerical length of HJ. Answer: HJ = Submit Answer attempt 1 out of 2

Identify the statement as true or false and justify your answer. Plane M is perpendicular to line s through point Q. Therefore it is the only plane perpendicular to s through point Q. a. False; If a line is perpendicular to a plane, any line perpendicular to that line at the point of intersection of the line and the plane is contained by the plane. b. True; If a line is perpendicular to a plane, any line perpendicular to that line at the point of intersection of the line and the plane is contained by the plane. c. True; Given a point on a line, there is one and only one plane perpendicular to the line through that point. d. False; Given a point on a line, there is one and only one plane perpendicular to the line through that point.

3. Helen of Troy was said to have been so beautiful that her face could launch a thousand ships. A table having this fable as its basis is shown here. Number of times Helen looked out her window, X Number of ships launched, y 1 2 3 4 1,000 2,000 3,000 4,000 a) Write a formula for this function. b) Solve the formula for x. c) How do x and y vary with respect to each other?