Answer:
[tex]y = \frac{7}{4}x +14[/tex]
Step-by-step explanation:
Given
[tex]y = \frac{7}{4}x + 4[/tex]
Required
Determine the equation of line that passes through (-8,0) and parallel to [tex]y = \frac{7}{4}x + 4[/tex]
Parallel lines have the same slope.
In [tex]y = \frac{7}{4}x + 4[/tex]
The slope, m is
[tex]m = \frac{7}{4}[/tex]
because the general form of a linear equation is:
[tex]y = mx + b[/tex]
Where
[tex]m = slope[/tex]
So, by comparison:
[tex]m = \frac{7}{4}[/tex]
Next, is to determine the equation of line through (-8,0)
This is calculated using:
[tex]y - y_1 = m(x - x_1)[/tex]
Where
[tex]m = \frac{7}{4}[/tex]
[tex](x_1,y_1) = (-8,0)[/tex]
So, we have:
[tex]y - 0 = \frac{7}{4}(x -(-8))[/tex]
[tex]y - 0 = \frac{7}{4}(x +8)[/tex]
[tex]y - 0 = \frac{7}{4}x +\frac{7}{4}*8[/tex]
[tex]y - 0 = \frac{7}{4}x +7*2[/tex]
[tex]y - 0 = \frac{7}{4}x +14[/tex]
[tex]y = \frac{7}{4}x +14[/tex]
