Question

Write the slope-intercept form of the equation of the line described. 10.) through: ( 5 , 5 ) , perpendicular to Y= -5x +3

Answer 1

To find the line equation perpendicular to the line equation y = -5x + 3, we need to know that the product of the slopes of two linear equation must be = -1. Then, the slope of the line perpendicular to y = -5x + 3 is:

m1 = -5x ---> m2 = 1/5, so m1 * m2 = -5 * 1/5 = -1.

As we can see, the new slope is the inverse and the reciprocal of the original slope.

Then, we have that passes through the point (5, 5). For this, we can use the Point-Slope Form of the line:

`y-y_1=m(x-x_(1))`

Where, x1 = 5, and y1 = 5. Hence:

`y-5=(1)/(5)(x-5)\Rightarrow y-5_{}=(1)/(5)x-1\Rightarrow y=(1)/(5)x-1+5`

Therefore, the line is:

`y=(1)/(5)x+4`