Question

Find the equation of the line with given slope and containing the given point. Write equation in slope-intercept form m= -1/4, point (-8, 3)

Answer 1

Recall that the slope-intercept form of a line equation is in the form

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

Given that we have the slope m = -1/4, and point (-8,3), substitute these two and solve for the y-intercept

`\begin{gathered} m=-(1)/(4) \\ (x,y)=(-8,3) \\ \\ y=mx+b \\ 3=\Big(-(1)/(4)\Big)(-8)+b \\ 3=(-8)/(-4)+b \\ 3=2+b \\ 3-2=b \\ 1=b \\ b=1 \end{gathered}`

We now have solved for the y-intercept, with m = -1/4, and b = 1, the equation of the line is

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