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cluponka [151]
3 years ago
10

Write an equation for the line in slope intercept form to parallel to -x + 3y =-2 that contains the point (12,7)

Mathematics
1 answer:
kvasek [131]3 years ago
3 0

The parallel lines have the same slope.

The slope-intercept form:

y=mx+b

m - slope

b - y-intercept

We have

-x+3y=-2\qquad|\text{add x to both sides}\\\\3y=x-2\qquad|\text{divide both sides by 3}\\\\y=\dfrac{1}{3}x-\dfrac{2}{3}\to m=\dfrac{1}{3}

Therefore searched line equation is:

y=\dfrac{1}{3}x+b

The line passes through point (12, 7). Put the coordinates of the point into the equation of the line:

7=\dfrac{1}{3}(12)+b\\\\7=4+b\qquad|\text{subtract 4 from both sides}\\\\3=b\to b=3

Answer: y=\dfrac{1}{3}x+3

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