Question

5) . Write theequation of a line in slope-intercept form.

Answer 1

Step-by-step explanation

Given the two points

`\begin{gathered} (x_1,y_1)=(-2,4) \\ (x_2,y_2)=(-1,1) \end{gathered}`

The rise and run of the line is given as;

`m=\frac{\text{rise}}{run}=(y_2-y_1)/(x_2-x_1)=(1-4)/(-1-(-2))=-(3)/(1)=-3^{}_{}`

Recall, the equation of a line in slope-intercept form is given as;

`y=mx+c`

Since we know the value of m, we can find the value of c by using one of the points above.

When x=-2, y= 4. Therefore;

`\begin{gathered} 4=-3(-2)+c \\ 4=6+c \\ c=4-6 \\ c=-2 \end{gathered}`

We then insert m and c into the slope-intercept equation.

Answer:

`y=-3x-2`