Question

a. y = 3x – 4 What is the slope? What is the y-intercept? Graph the equation.b. What is the equation of the line in slope intercept form that passes through (8, 7) and (6, -1)?

Answer 1

Part a

we have the equation

$y=3x-4$

so

The slope is m=3

The y-intercept is the point (0,-4)------> the value of b=-4

To graph the line, we need two points

we have one point (0,-4) y-intercept

Find out another point

For x=1

$\begin{gathered} y=3(1)-4 \\ y=-1 \end{gathered}$

The other point is (1,-1)

so

Plot the points (0,-4) and (1,-10

join them to graph the line

using a graphing tool

see the figure below

Part B

The equation of the line in slope-intercept form is given by

$y=mx+b$

we have (8, 7) and (6, -1)

step 1

Find out the slope

$\begin{gathered} m=\frac{-1-7}{6-8} \\ \\ m=\frac{-8}{-2} \\ \\ m=4 \end{gathered}$

step 2

Substitute given values

we have

m=2

point (8,7)

$\begin{gathered} 7=8(2)+b \\ solve\text{ for b} \\ 7=16+b \\ b=-9 \end{gathered}$

therefore

The equation of the line is

$y=2x-9$