given the equation y = -7/4 (x - 11) + 9, what is the slope and the obvious point on the graph and determine the equation of the line perpendicular to the above line, sharing the same x-intercept

Answer 1

The slope is -7/4 from

y = -7/4(x -11) + 9

y = -7/4x + 77/4 + 36/4

y = -7/4x + 113/4

Find the intercepts by setting x = 0 for the y intercept, then y = 0 to find the x intercept

0 = -7/4x + 113/4

Add 7/4x to both sides of the equation

7/4x = 113/4

Multiply both sides by 4/7 to solve for x

x = (4/7)(113/4)

x = 113/7 when y = 0

For the line above, the intercepts are (0, 113/4) and (113/7, 0)

The slope of the line perpendicular to

y = -7/4x + 113/4

Is the positive inverse of -7/4, so

m = 4/7

Use the x intercept coordinates, (113/7, 0) to find b,

0 = 4/7(113/7) + b

0 = 452/49 + b

Subtract 452/49 from both sides of the equation

-452/49 = b

y = 4/7x - 452/49 is perpendicular to the line y = -7/4(x -11) + 9

y = 4/7x - 452/49 is perpendicular to the line y = -7/4x + 113/4

You can plot both lines at Desmos.com to see that they share the same x intercept and are perpendicular.

I hope you find this useful if you have any questions send me a message.

Answer 2

y = -7/4 (x - 11) + 9

That's what we start with. If I carry out the operations it becomes

y = (-7/4) x + (77 / 4) + 9 = (-7 / 4) x + (113 / 4)

That's about as much as I can simplify. A line perpendicular to this one will have slope equal to the negative reciprocal of the slope you start with. So m = (4 / 7). You also need the same x-intercept, which occurs when y= 0. For the equation you start with, that's

0 = (-7 / 4) x + (113 / 4) and you must solve for x.

7x = 113

or x = 19 when y = 0.

Put together what we know so far and get

0 = 19 (4 / 7) + y-intercept

so y-intercept = -76 / 7

And the equation you seek, perpendicular to the original line with the same x-intercept is

y = (4 / 7) x - (76 / 7) or

y = (4 / 7) (x - 19)