Question

Determine the equation of the line that is parallel to y=5x+4 and that passes through (8,-2)

Answer 1

The equation of line parallel to y = 5x + 4 is

y = 5x - 42

Explanation:

The two parallel lines have equal slope.

The given equation of a line is y = 5x + 4

Here slope m = 5

The line parallel to this line have same slope.

The equation of new line is, y = 5x + c

Where c is a constant

To find the equation of line

y = 5x + c ------(1)

This line passes through (8,-2)

Substitute value of x and y in equation (1) we get

-2 = (5*8) + c

-2 = 40 + c

c = -42

Therefore the equation of line parallel to y = 5x + 4 is

y = 5x - 42

Answer 2

The equation of the line in slope intercept form is; y = 5x-42

Step-by-step explanation:

Parallel lines have identical or equal slopes. This implies that the form of the equation of the line will be;

y=5x+c

Since this line passes through (8,-2), we determine the value c by substituting x with 8 and y with -2. We solve the equation;

-2 =5(8)+c to obtain c = -42

The equation of the line in slope-intercept form is thus y = 5x-42