Question

I inserted a picture of the question, can you please make it fast

Answer 1

Given:

Points on the line (5,2) and (-3,-2)

The slope-interept form of an equation is written as

`\begin{gathered} y=mx+b \\ \text{where} \\ m\text{ is the slope of the line} \\ b\text{ is the y-intercept} \end{gathered}`

Solve first for the slope

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ \text{where} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are the points in the line} \\ \\ (x_1,y_1)=(5,2) \\ (x_2,y_2)=(-3,-2) \\ \\ \text{Substitute and the slope is} \\ m=(y_2-y_1)/(x_2-x_1) \\ m=(-2-2)/(-3-5) \\ m=(-4)/(-8) \\ m=(1)/(2) \\ \\ \text{The slope of the line is }(1)/(2) \end{gathered}`

Now that we have solved for the slope, use any of the two points to solve for the y-intercept. For this case, we will use (5,2) but using (-3,-2) will work just as well.

`\begin{gathered} y=mx+b \\ \text{Substitute} \\ m=(1)/(2),x=5,\text{ and }y=2 \\ \\ y=mx+b \\ 2=((1)/(2))(5)+b \\ 2=(5)/(2)+b \\ 2-(5)/(2)=b \\ (4)/(2)-(5)/(2)=b \\ b=-(1)/(2) \end{gathered}`

Putting it together, with m = 1/2 and b = -1/2, the equation of the line is

`y=(1)/(2)x-(1)/(2)`