Graphing Linear Equations

Given the equation 4x - 5y = 20, find the slope of the line.

4x - 5y = 20 -5y = -4x + 20 y = 4/5x - 4 m = 4/5

Describe the line y = -2.

This is a horizontal line at the y value of -2.

Describe the line y + 1 = 1/5(x - 4).

This is a shallow uphill line that has a point (4, -1)

Describe the line x = 4.

This is a vertical line at the x value of 4.

Describe the line y = -9x + 1.

This is a very steep downhill line that crosses the y axis at (0, 1).

Given the equation 3x -2y = 12, describe how you would graph the line.

We could rewrite the equation in slope intercept form and use the slope and y intercept to graph the line. Or, we could find the x and y intercept and use them to graph the line (substitute zero in for x to find the y intercept and then substitute zero in for y to find the x intercept).

Calculate the slope (rate of change) of the line that passes through the following 2 points - (-2, 6) (4, -3)

m = (-3 - 6) over (4 - -2) m = -9/6 m = -3/2

Write the equation of the line that passes through the following 2 points in standard form - (2, 6) (-2, 3)

m = (3 - 6) over (-2 - 2) m = -3/-4 = 3/4 y - 6 = 3/4(x - 2) y - 6 = 3/4x - 3/2 y = 3/4x + 9/2 4y = 3x + 18 -3x + 4y = 18

Calculate the slope (rate of change) of the line that passes through the following 2 points - (2, 4) (-3, 4)

m = (4 - 4) over (-3 - 2) m = 0/-5 m = 0 horizontal line

Calculate the slope (rate of change) of the line that passes through the following 2 points - (2, -4) (3, 5)

m = (5- -4) over (3 - 2) m = 9/1

Calculate the slope (rate of change) of the line that passes through the following 2 points - (5, -6) (5, 8)

m = (8 - -6) over (5 - 5) m = 14/0 undefined - can not divide by zero vertical line

Given the equation y - 3 = -1/2(x + 4), describe how you would graph the line.

m = -1/2 a point is (-4, 3) place a dot on the graph at the point (-4, 3) and move up 1 and left 2 and continue that pattern. You could also move down 1 and right 2.

Name the slope and a point from the given equation - y - 5 = -2/3(x + 7)

m = -2/3 point = (-7, 5)

What is the slope and y intercept of the line y = -3/4x - 9

m = -3/4 b = -9

Write the equation y = 1/3x - 4 in point slope form using the point (6, -2).

m = 1/3 y + 2 = 1/2(x - 6)

Given the equation y = 2x + 4, describe how you would graph the line.

m = 2 b = 4 begin at the y intercept of 4 and then from there move up 2, right 1 and continue that pattern. You could also move down 2, left 1.

Calculate the average rate of change. Jude charges an amount per hour she cleans houses plus a driving fee. If she worked 3 hours and charged $45 and worked 6 hours and charged $75, what is her hourly rate in dollars per hour?

rate of change = (75 - 45) over (6 - 3) rate of change = 30/3 rate of change = $10 per hour

Find the x and y intercepts of the equation -2x + 5y = -30

x intercept -2x + 5(0) = -30 -2x = -30 x = 15 y intercept -2(0) + 5y = -30 5y = -30 y = -6

Find the x and y intercepts of the equation 4x - 5y = 20

x intercept 4x - 5(0) = 20 4x = 20 x = 5 y intercept 4(0) - 5y = 20 -5y = 20 y = -4

Write the equation of the line that is parallel to the line y = 1/5x + 3 and has the point (2, -3) in slope intercept form.

y + 3 = 1/5(x - 2) y + 3 = 1/5x - 2/5 y = 1/5x - 17/5

Write the equation y - 3 = 2(x + 4) in standard form.

y - 3 = 2(x + 4) y - 3 = 2x + 8 y = 2x + 11 -2x + y = 11

Write the equation of the line that has a slope of -2/3 and a y-intercept of 4 in standard form.

y = -2/3x + 4 2/3x + y = 4 2x + 3y = 12

Write the equation of the line that has a slope of -3 and a y-intercept of -8 in slope intercept form.

y = -3x - 8

Write the equation y = 2/7x - 2 in standard form.

y = 2/7x - 2 7y = 2x - 14 -2x + 7y = -14

Write the equation of the line that has a slope of 3 and a y-intercept of 2 in standard form.

y = 3x + 2 -3x + y = 2