Question

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Answer 1

Answer:

-5, 5

Step-by-step explanation:

The line in this problem can be  written in the form

$y=mx+q$ (1)

where:

$m=\frac{2}{3}$ is the slope

q is the y-intercept

We know that the line passes through the point (-2,5), so substituting these values into eq.(1), we find the value of the y-intercept:

$q=y-mx=5-(\frac{2}{3})(-2)=5+\frac{4}{3}=\frac{19}{3}$

So the equation of the line is

$y=\frac{2}{3}x+\frac{19}{3}$ (2)

Now we know that point A has coordinates

A(x,3)

So by substituting into eq.(2), we find the missing x-coordinate:

$3=\frac{2}{3}x+\frac{19}{3}\\9=2x+19\\x=\frac{9-19}{2}=-5$

Similarly, point B has coordinates

B(-2,y)

so substituting into eq(2), we find the missing y-coordinate:

$y=\frac{2}{3}(-2)+\frac{19}{3}=5$