Question

On a coordinate plane, a line goes through (negative 5, negative 4) and (0, negative 3). A point is at (negative 2, 2).
What is the equation of the line that is parallel to the given line and passes through the point (–2, 2)?

y = One-fifthx + 4
y = One-fifthx + Twelve-fifths
y = –5x + 4
y = –5x + Twelve-fifths

Answer 1

Rewriting the point-slope equation of the line, the equation of the line that is parallel to the given line is: y = 1/5x + 12/5.

What is the Point-Slope Equation?

The point-slope equation is given as y - b = m(x - a), where m is the slope (change in y/change in x), and (a, b) is a point.

Find the slope of the line that passes through, (-5, -4) and (0, -3):

Slope = change in y/change in x = (-3 -(-4)) / (0 -(-5)) = 1/5

Slopeof parallel lines are equal, teherfore, the slope of the line that passes through (-2, 2) would be 1/5.

Substitite (a, b) = (-2, 2) and m = 1/5 into y - b = m(x - a):

y - 2 = 1/5(x -(-2)

y - 2 = 1/5(x + 2)

Rewroite in slope-inetrcept form

y - 2 = 1/5x + 2/5

y = 1/5x + 2/5 + 2

y = 1/5x + 12/5

Therefore, rewriting the point-slope equation of the line, the equation of the line that is parallel to the given line is: y = 1/5x + 12/5.

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