Question

Graph a line that contains the point 1 (3,-6) and has a slope of 2

Answer 1

$y=2x-12\rightarrow eq\text{uation of the line}$

Explanation

Step 1

Let

slope=2

point (3,-6)

$\begin{gathered} y-y_1=m(x-x_1) \\ \end{gathered}$

replace.

$\begin{gathered} y-y_1=m(x-x_1) \\ y-(-6)=2(x-3) \\ y+6=2x-6 \\ \text{subtract 6 in both sides} \\ y+6-6=2x-6-6 \\ y=2x-12\rightarrow eq\text{uation of the line} \end{gathered}$

Step 2

now, fidn two points of the line

a) when x= 0

$\begin{gathered} y=2x-12 \\ y=2\cdot0-12 \\ y=0-12 \\ y=-12 \\ P1(0,-12) \end{gathered}$

b) when x= 5

$\begin{gathered} y=2x-12 \\ y=2\cdot5-12 \\ y=10-12 \\ y=-2 \\ P2(5,-2) \end{gathered}$

Step 3

finally, draw the lines by using P1 and P2

I hope this helps you