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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
A line passes through point (-2, 5) and has a slope of . Points A(x, 3) and B(-2, y) lie on the line.
The value of x is
, and the value of y is
.

Type the correct answer in each box Use numerals instead of words If necessary use for the fraction bars A line passes through point 2 5 and has a slope of Poin class=

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skyluke89

Answer:

-5, 5

Step-by-step explanation:

The line in this problem can be  written in the form

[tex]y=mx+q[/tex] (1)

where:

[tex]m=\frac{2}{3}[/tex] 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:

[tex]q=y-mx=5-(\frac{2}{3})(-2)=5+\frac{4}{3}=\frac{19}{3}[/tex]

So the equation of the line is

[tex]y=\frac{2}{3}x+\frac{19}{3}[/tex] (2)

Now we know that point A has coordinates

A(x,3)

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

[tex]3=\frac{2}{3}x+\frac{19}{3}\\9=2x+19\\x=\frac{9-19}{2}=-5[/tex]

Similarly, point B has coordinates

B(-2,y)

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

[tex]y=\frac{2}{3}(-2)+\frac{19}{3}=5[/tex]

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