Write the equation of the line perpendicular to y=1/4x+7 and passes through (2,-9)

Given:

points (2 , -9)

x1 = 2

y= -9

Determine the equation of the line perpendicular to ¼x + 7

Solution:

When we say perpendicular, that means that they have the same slope which ¼, represented in the equation given. The equation is represented in slope-intercept form written as, 

y = mx + b

m = ¼

Hence, we can write the equation of the line to either similar to the given in slope-intercept form, or in point-slope form represented as,

y - y1 = m (x - x1)

Substitute the given values of m, x1,and y1 to the point-slope form equation.

y - (-9) = ¼ (x - 2)

Point-slope form: y + 9 = ¼ (x -2)

To change in slope-intercept form, we simply transpose 9 on the other side of the equation, hence we must take note that when transposing a number, the sign changes.

y = ¼x - ½ - 9

9 can be written as 18/2 in order to easily subtract the given fraction.

y = ¼x - ½ - 18/2

Slope-intercept form: y = ¼x - 19/2

Final answer:

Point-slope form: y + 9 = ¼ (x -2)

Slope-intercept form: y = ¼x - 19/2