How do you find a slope for the problem x = -4y?

justcause | Middle School Teacher | (Level 1) Adjunct Educator

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If you are plotting the points/line and demonstrating the slope on a graph, then the previous answer is correct. You can set up a table.

However, like the previous answer suggests, the equation must be in slope-intercept format, which is y=mx+b. Since you have x = -4y, you have to do a little simple algebra to flip it around.

If x= -4y
Divide by -4 on both sides.
You get x/-4 = y OR y=x/-4, which is now in slope-intercept format.
The slope (m) is found in front of x and since x/-4 is the same as -1/4x, then you have a slope of -1/4.
This can be seen in the previous post's table. When y (rise) equals -1/2, x (run) = 2. Rise/run = -1/2 /2, which also equals -1/4.

marilynn07 | High School Teacher | (Level 3) Associate Educator

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Basically, you can set up a table to solve for the y value.  You pick the x value.

x | y

0 | 0

1 | -1/4

2 | -1/2

Then you can plot these points on your graph.

Using the slope-intercept formula: y = mx + b You can then determine the slope of the line. Remember rise/run.

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

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The slope of a line ax + by + c = 0 is the rate at which y changes with respect to x.

The slope is given by the derivative `dy/dx` .

For the relation x = -4y, to determine the required slope, take the derivative of both sides with respect to x.

`dx/dx = (d(-4y))/dy`

`1 = -4*dy/dx`

`dy/dx = -1/4`

The required slope of the line x = -4y is -1/4