Identify an equation slope-intercept form for the line parallel to y=5x+2 that passes through (-6,-1)

Given:

points ( -6, -1)

x1 = -6

y1 = -1

Determine the equation of the line in slope-intercept parallel to y = 5x + 2

Equation for slope-intercept form:
y = mx  + b

Solution:

The given line is already in slope-intercept form, hence we know that is equal to the slope, and since it is stated that they are parallel, that means that they have the same slope.

m = 5

Now in order to write the slope-intercept form of the given points, we must equate it first in point-slope form.

Point-slope form:

y - y1 =m (x - x1)

Substitute the given values of x1, y1, and m.

y - (-1) = 5(x - (-6))

y + 1 = 5(x + 6)

Distribute the value of 5 to each value inside the parenthesis, and transpose 1 on the other side of the equation, hence we must take note that in transposing a number, the sign changes.

y + 1 = 5x + 30

y = 5x + 30 -1

y = 5x + 29

Final answer:
Slope-intercept form: y = 5x + 29