Aline is parallel to y = 4x + 1 and intersects the point (-2, -5) what is the equation of this parallel line?

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

The equation of the given line is

y= 4x + 1

Comparing with the slope intercept form, slope = 4

If two lines are parallel, it means that they have the same slope. Therefore, the slope of the line passing through (-2, - 5) is 4

To determine the intercept, we would substitute m = 4, x = - 2 and y = -5 into y = mx + c. It becomes

- 5 = 4 × - 2 + c = - 8 + c

c = - 5 + 8 = 3

The equation becomes

y = 4x + 3

Step-by-step explanation:

any eq. of line parallel to y=4x+1 is

y=4x+a

it passes through (-2,-5)

so -5=4(-2)+a

a=-5+8

a=3

reqd. eq. is y=4x+3

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