Question

plot four lines. Each lines should pass through the point on the y-axis

Answer 1

we have that for each line, the y-intercept is the point (0,-2), then, we can use this point with another to find the slope, and then the equation of the line that passes through those points.

First, lets take the point (-4,3), then:

$\begin{gathered} slope\colon \\ m=\frac{3-(-2)}{-4-0}=\frac{3+2}{-4}=-\frac{5}{4} \\ equation\colon \\ y=-\frac{5}{4}x-2 \end{gathered}$

for the point (1,-4), we have:

$\begin{gathered} slope\colon \\ m=\frac{-4-(-2)}{1-0}=\frac{-4+2}{1}=-2 \\ equation\colon \\ y=-2x-2 \end{gathered}$

finally, for the point (-3,-5), we get:

$\begin{gathered} slope\colon \\ m=\frac{-5-(-2)}{-3-0}=\frac{-5+2}{-3}=\frac{-3}{-3}=1 \\ equation\colon \\ y=x-2 \end{gathered}$

therefore, the missing lines are

y=x-2

y=-2x-2

y=-5/4x-2