Which equation represents a line which is perpendicular to the line 6x-5y=-25

Question

Which line is perpendicular to the line 6x-5y=-25

Answer 1

You have to know the types of linear equations

1. standard form Ax+By=c

2. Slope-intercept form y= mx +b where

m → slope

b → y-intercept

Also you have to know

a. When you have two lines are parallel this mean have the same (equal) slope

b. When you have two lines are perpendicular this means have negative reciprocal slope

Now we can solve the problem:

Rewrite the equation 6x- 5y =- 25 from standard form to slope -intercept form by solve for y

y= 6/5 x + 5

slope. m = 6/5

negative reciprocal slope -5/6

then the new equation

y = -5/6 x + b

Answer 2

When the equation of a line is given in Standard Format (Ax+By=C), the slope m=(-A/B).

Perpendicular lines have slopes that are the negative reciprocal of each other. That is, (m) and (-1/m). So, for lines in Standard Format, that is (-A/B) and (B/A).

Here m=(6/5). The slope of all perpendicular lines is (-5/6), so all perpendicular lines have an equation that looks like (in Standard Format):

5x + 6y = D [and a point is needed to determine the value of D and which parallel line solves the problem.