Question

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

Answer 1

`y=(3)/(4)x+1`

Step-by-step 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}}=(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}}=(y_2-y_1)/(x_2-x_1) \\ \text{slope}=(-5-(-11))/(-8-(-16))=(-5+11)/(-8+16)=(6)/(8)=(3)/(4) \\ \text{slope}=(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)=(3)/(4)(x-(-16)) \\ y+11=(3)/(4)x+(48)/(4) \\ y+11=(3)/(4)x+12 \\ \text{subtract 11 in both sides} \\ y+11-11=(3)/(4)x+12-11 \\ y=(3)/(4)x+1 \end{gathered}`

I hope this helps you