Question

The third method for graphing the solution set is to use the slope and y-intercept. Answer the following:

a) Find the slope and the y-intercept of the line formed by the following equation. Provide an in-between step: 9x - 3y = 15.

b) Explain how you would use the slope and y-intercept to graph the line represented by this equation.

Answer 1

Given straight line is $9x-3y=15 ....(1)$

To find the slope and y intercept we reduce the equation in (1) to$y= mx+c$

From (1)

$-3y=15-9x$

Dividing with (-3) we get

$$y=-5+3x$$

Therefore, slope $m=3$

y intercept $c= -5$

b) To draw the graph of the straight line in (1), we need two points.

One point is $(0,-5)$

(Since the straight line cuts the y axis at $c=-5$

To find the second point we use slope $m=3$

Slope

$$m=\>(rise)/(run)$$

$= \>3 /1$

Therefore, rising 3 units above $-5,$ run will be $1$

$\Rightarrow$ we get a point $(1,-2)$.

Joining the points $(0,-5)$ and $(1,-2)$ we get the graph of the straight line $9x-3y=15.$