Question

Write an equation in slope-intercept form for the line that satisfies the given conditions.a)x-intercept = 3, y-intercept = -2

Answer 1

We know that the slope-intercept form of the equation of the line is:

$y=mx+b$

since the y-intercept is -2, then we have that b = -2.

To find the slope, we can use the x-intercept doing the substitution of the point (3,0) on the previous equation to get the following:

$\begin{gathered} (x,y)=(3,0) \\ b=-2 \\ \Rightarrow0=m(3)+(-2)=3m-2 \\ \Rightarrow0=3m-2 \end{gathered}$

now, solving for m we get the following:

$\begin{gathered} 3m-2=0 \\ \Rightarrow3m=2 \\ \Rightarrow m=\frac{2}{3} \end{gathered}$

now that we have that m = 2/3 and b = -2, the equation in slope-intercept form is:

$y=\frac{2}{3}x-2$