Question

Write the slope intercept form of the equation of the line described

Through (-1,-4), parallel to y=7x-4

Answer 1

For this case we have that by definition, the equation of the line in the slope-intersection form is given by:

$y = mx + b$

Where:

m: It is the slope

b: It is the cut point with the y axis

We have the following equation:

$y = 7x-4$

So the slope is $m = 7$

By definition, if two lines are parallel then their slopes are equal, so a parallel line would be of the form:

$y = 7x + b$

We substitute the given point and find "b":

$-4 = 7 (-1) + b\\-4 = -7 + b\\-4 + 7 = b\\b = 3$

Finally, the equation is:

$y = 7x + 3$

Answer:

$y = 7x + 3$