Question

write the equation in slope intercept form for a line that will pass through (-6,7) and have a slope of 1/2.

Answer 1

The equation in slope intercept form for a line that will pass through (-6,7) and have a slope of 1/2 is;

`y=(1)/(2)x+10`

Step-by-step explanation:

We want to find the equation of the line in slope-intercept form;

`\begin{gathered} y=mx+b \\ \text{where;} \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}`

Given;

`\begin{gathered} m=(1)/(2) \\ \text{ point (}x_1,y_1)=(-6,7) \end{gathered}`

Substituting the values into the point slope equation and simplifying;

`\begin{gathered} y-y_1=m(x-x_1) \\ y-7=(1)/(2)(x-(-6)) \\ y-7=(1)/(2)(x+6) \\ y-7=(1)/(2)x+3 \\ y=(1)/(2)x+3+7 \\ y=(1)/(2)x+10 \end{gathered}`

The equation in slope intercept form for a line that will pass through (-6,7) and have a slope of 1/2 is;

`y=(1)/(2)x+10`