find an equation of the line

Question

Find an equation of the line through (5,2) and is perpendicular to y=5x-9

Answer 1

First, let's find the slope of the equation y = 5x -9.

This equation is in the form y = mx+b, also called slope-intercept form.

M denotes the slope.

Therefore, in this equation, m = 5.

 

If a line is perpendicular to another line, its slope is the negative reciprocal of the line to which it is perpendicular.

Therefore, the negative reciprocal of 5 is -1/5.

 

Now we plug in the x-value given above (5), the y-value (2), and the slope, m = -1/5, into the form y = mx +b.

We must solve for b, since that value is unknown. We cannot simply give the equation of the line without knowing what b is.

So, we do:

2 = (-1/5)(5) + b

Solving for b, we get that b = 3.

 

Now we plug b = 3 into the equation y = mx +b, along with m = -1/5.

This yields y = (-1/5)x + 3.

 

This is the equation of the line that passes through (5, 2) and is perpendicular to y = 5x - 9.

If we wanted to check this equation that we found, we can plug either y = 2 or x = 5 into the equation, solve for the unknown variable (x if you plugged in the y-value, or y if you plugged in the x-value), and attain the other coordinate point of the ordered pair.