Question

2. X -16 -8 0 8 16 y -11 -5 1 7 13, find the equation of the line

Answer 1

$y=\frac{3}{4}x+1$

Explanation

Step 1

find the slope of the line:

when you know 2 points of a line P1 and P2, the slope is given by:

$\begin{gathered} \text{slope}=\frac{change\text{ in y}}{\text{change in x}}=\frac{y_2-y_1}{x_2-x_1} \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \end{gathered}$

Let

P1(-16,-11)

P2(-8,-5)

replace

$\begin{gathered} \text{slope}=\frac{change\text{ in y}}{\text{change in x}}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{-5-(-11)}{-8-(-16)}=\frac{-5+11}{-8+16}=\frac{6}{8}=\frac{3}{4} \\ \text{slope}=\frac{3}{4} \end{gathered}$

Step 2

find the equation of the line,use:

$\begin{gathered} y-y_1=slope(x-x_1) \\ \text{replace} \\ y-(-11)=\frac{3}{4}(x-(-16)) \\ y+11=\frac{3}{4}x+\frac{48}{4} \\ y+11=\frac{3}{4}x+12 \\ \text{subtract 11 in both sides} \\ y+11-11=\frac{3}{4}x+12-11 \\ y=\frac{3}{4}x+1 \end{gathered}$

I hope this helps you