Question

Enter the equation of the line in slope-intercept form.

Answer 1

Answer:

$y = \frac{7}{4}x +14$

Step-by-step explanation:

Given

$y = \frac{7}{4}x + 4$

Required

Determine the equation of line that passes through (-8,0) and parallel to $y = \frac{7}{4}x + 4$

Parallel lines have the same slope.

In $y = \frac{7}{4}x + 4$

The slope, m is

$m = \frac{7}{4}$

because the general form of a linear equation is:

$y = mx + b$

Where

$m = slope$

So, by comparison:

$m = \frac{7}{4}$

Next, is to determine the equation of line through (-8,0)

This is calculated using:

$y - y_1 = m(x - x_1)$

Where

$m = \frac{7}{4}$

$(x_1,y_1) = (-8,0)$

So, we have:

$y - 0 = \frac{7}{4}(x -(-8))$

$y - 0 = \frac{7}{4}(x +8)$

$y - 0 = \frac{7}{4}x +\frac{7}{4}*8$

$y - 0 = \frac{7}{4}x +7*2$

$y - 0 = \frac{7}{4}x +14$

$y = \frac{7}{4}x +14$