Find the equation of the line ALGEBRAICALLY that is perpendicular to the line 5x - 8y + 24 = 0 and has the same x-intercept as the line 7x - 12y - 70 = 0.

Step-by-step explanation:

There are several things we need to do/know to figure this out. First we have to know that the perpendicular slope to a line is the opposite reciprocal of the slope of which it is perpendicular (did that make sense?!). In other words, we have to find the slope of the line 5x - 8y + 24 = 0 and then take the opposite reciprocal of it. Solving for y:

with a slope of 5/8. The perpendicular slope, then, is -8/5. So we have m now in y = mx + b. Now onto the second equation...

The equation for which we need the same x-intercept is 7x - 12y - 70 = 0. The x-intercept exists when y = 0, so filling in a 0 for y:

7x - 12(0) = 70 and

x = 10. Now we know x. We also know, however, that when x = 10, y = 0, so we have everything we need to sub into the linear equation and solve for b:

0 = -8/5(10) + b and

0 = -16 + b so

b = 16 and the equation we are looking for is

y = -8/5x + 16

x= 149. 24+7=31. 180-31=149

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