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Which choice is the equation of a line that passes through (9, -3) and is parallel to the line represented by this equation? y=5/3x-4

Answer :

calculista

Answer:

[tex]y+3=\frac{5}{3}(x-9)[/tex]  or  [tex]y=\frac{5}{3}x-18[/tex]

Step-by-step explanation:

step 1

Find the slope of the line parallel to the given line

we know that

If two lines are parallel, then their slopes are the same

we have

[tex]y=\frac{5}{3}x-4[/tex]

therefore

The slope m of the line parallel to the given line is

[tex]m=\frac{5}{3}[/tex]

step 2

Find the equation of the line in point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=\frac{5}{3}[/tex]

[tex]point\ (9,-3)[/tex]

substitute

[tex]y+3=\frac{5}{3}(x-9)[/tex] ----> equation of the line in point slope form

step 3

Find the equation of the line in slope intercept form

[tex]y=mx+b[/tex]

we have

[tex]y+3=\frac{5}{3}(x-9)[/tex]

Isolate the variable y

[tex]y+3=\frac{5}{3}x-15[/tex]

[tex]y=\frac{5}{3}x-15-3[/tex]

[tex]y=\frac{5}{3}x-18[/tex]

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