Parallel Lines Equation

Question

Write the equation for the line parallel to 4y - 7x = 8 and passes through (-4,0)



Answer 1

The equation of the line is y = 7/4x + 7.

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Begin by rewriting the equation 4y - 7x = 8 in slope-intercept form.

Add 7x to both sides

4y - 7x + 7x = 8 + 7x

4y = 8 + 7x

4y = 7x + 8 (commutative property)

Divide all terms by 4 to isolate y.

(4y)/4 = (7x)/4 + (8)/4

y = 7/4x + 2

Since we want to find a line that is parallel, we don't need to change the slope. We can continue by writing slope-intercept form using the slope only.

y = 7/4x + b

Substitute (-4, 0) for x and y

y = 7/4x + b

0 = 7/4(-4) + b

Solve for b

0 = -7 + b (multiply 7/4 by -4)

0 + 7 = -7 + 7 + b

7 = b

Now that we know the slope (7/4) and the y-intercept (7), we can write the slope-intercept form.

y = 7/4x + 7.