63.8k views
5 votes
I inserted a picture of the question, can you please make it fast

I inserted a picture of the question, can you please make it fast-example-1
User AgentDBA
by
7.5k points

1 Answer

0 votes

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)

User Selvan
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories