Question

What is the equation in slope-intercept form of the line that passes through the point(-4,7) and is perpendicular to y=4x+15

Answer 1

The equation of the line perpendicular to y = 4x + 15 and passing through the point (-4,7) is y = -1/4x - 8.

Step-by-step explanation:

To find the equation of a line that is perpendicular to a given line, we need to find the negative reciprocal of the given line's slope. The given line is y = 4x + 15, so the slope of the given line is 4. The negative reciprocal of 4 is -1/4. Since the new line passes through the point (-4,7), we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

1. Substitute the values of x1, y1, and m into the equation.
2. Simplify the equation to slope-intercept form (y = mx + b).

After substituting the values, the equation of the line is y - 7 = -1/4(x - (-4)). Simplifying the equation gives us y - 7 = -1/4(x + 4). Converting to slope-intercept form, the equation is y = -1/4x - 8.

Answer 2

Step-by-step explanation:

First find the slope of the line y =4x + 15

slope = 4

Slope of the required line = -1/m = -1/4

(-4 , 7)

Slope point form: y - y1 = m(x - x1)

`y - 7 = (-1)/(4)(x - [-4])\\\\y -7 = (-1)/(4)(x + 4)\\\\y - 7 =(-1)/(4)x + 4*(-1)/(4)\\\\y - 7 =(-1)/(4)x-1\\\\y = (-1)/(4)x - 1 + 7\\\\y = (-1)/(4)x + 6`