What is the slope of a line that is perpendicular to the line whose equation is y=4x+1?

y - 4 x = 1

Step-by-step explanation:

y = 4 x + 1

Using the slope-intercept form, the slope is 4.

m = 4

The equation of a perpendicular line to y = 4 x + 1 must have a slope that is the negative reciprocal of the original slope.

m perpendicular = - 1/4

Step-by-step explanation:

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = y intercept

Slope, m = change in value of y on the vertical axis / change in value of x on the horizontal axis

From the information given,

comparing the equation given,

y=4x+1 with the slope intercept equation, y = mx + c

Slope, m = 4

When two slopes are perpendicular, their product is - 1

Let the slope of the perpendicular line to the one given by the above equation be m1. Therefore,

m * m1 = - 1

4 m1 = - 1

m1 = - 1/4

Inputting m1 = 4 into the slope intercept equation, it becomes

y = - 1/4*x + c

y = - x/4 + c