What is the equation of the line that passes through the point (7,6)(7,6) and has a slope of 0?

If you want to find the equation of line with a given a slope of

which goes through the point (,), you can simply use the point-slope formula to find the equation: ---Point-Slope Formula---

where is the slope, and is the given point

So lets use the Point-Slope Formula to find the equation of the line

Plug in , , and (these values are given)

Distribute

Multiply and to get

Add 7 to both sides to isolate y

Combine like terms and to get

Remove the zero terms

------------------------------------------------------------------------------------------------------------ Answer:

So the equation of the line with a slope of which goes through the point (,) is:

which is now in

form where the slope is and the y-intercept is

Notice if we graph the equation and plot the point (,), we get (note: if you need help with graphing, check out this solver)

Graph of through the point (,)

and we can see that the point lies on the line. Since we know the equation has a slope of and goes through the point (,), this verifies our answer.

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Kayla O.

asked • 01/06/21

1 Expert Answer

Karen J. answered • 01/06/21

Harvard Public Health Graduate for Math / Stats / R

Hi Kayla,

Let's start by writing 6x + 5y = 30 into a form we are familiar with, y = mx + b, where m is the slope and b is the y intercept.

5y = -6x + 30

y = (-6/5)x + 6

Now, we know that the slope of our original line is m = -6/5. To find the slope of the perpendicular line, we can take the negative reciprocal of the original line, which would be a new slope of 5/6.

Now we have the slope of the new line m = 5/6 and a point it passes through (-6, -7).

We can use y = mx + b again by plugging in our known values (x, y, m) to solve for b.

-7 = 5/6*(-6) + b

-7 = -5 + b

b = -2

So the equation of our new line is now

y = (5/6)x - 2