Question

Lines m and n are parallel. Line m is described by y=4x+2. Line n contains the point (1, -3). Which of the following is an equation for line n?
Lines m and n are parallel Line m is described by the equation y
A Oy-3 = 4(x + 1)
B. Oy-3=(x+1)
c. Oy+3 = 4(x - 1)
D.Oy+3 = 4(x - 1)

Answer 1

The equation of line m, in point-slope form is: y + 3 = 4(x - 1)

Recall:

• The slopes of parallel lines are equal to each other.

• Slope-intercept form equation is: y = mx + b, where m is slope and b is y-intercept.

• Point-slope form equation is: $y - y_1 = m(x - x_1)$ where, $(x_1, y_1)$ is a point and m is the slope.

Equation of line m is y = 4x + 2

Slope of line m is 4

Since line m and line n are parallel, both lines will have the same slope. Therefore, the slope of line n is 4.

To write the equation for line if it contains the point (1, -3), substitute $(x_1, y_1)$ = (1, -3) and m = 4 into $y - y_1 = m(x - x_1)$:

$y - (-3) = 4(x - 1)\\\\\mathbf{y + 3 = 4(x - 1)}$

Therefore, the equation of line n, in point-slope form is: y + 3 = 4(x - 1)

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