How do you find the slope of an equation?

Answer 1

How to find slope if you are given the equation of a line in slope-intercept form:

Slope intercept form is y = mx + b. m is the slope.

For example, the slope of the line y = 3x + 7 is 3. (3 is m in the equation y = mx + b.) Another example, the slope of the line y = (-5/4)x - 4 is -5/4.

If the line is in the form y = a number, then the slope is 0. For example, the slope of the line y = 3 is 0.

If the line is int the form x = a number, then the slope is undefined. For example, the slope of the line x = 5 is undefined.

How to find slope if you are given the equation of a line in point-slope form:

Point slope form is y - y1 = m(x - x1). m is the slope.

For example, the slope of the line y-6 = 2(x-7) is 2. Another example, the slope of the line y-5 = (3/2)(x+4) is 3/2.

How to find the slope if you are given the equation of a line in standard form:

Standard form is ax + by = c.

One way to find the slope if a line in standard form is to convert it to slope-intercept form (y=mx+b).

Here is an example using the line 3x + 8y = 28

3x + 8y = 28

First move the x to the other side by subtracting 3x from each side:

8y = 28 - 3x

Next, divide each side by 8 (all three terms must be divided by 8):

y = 28/8 - (3/8)x

After simplifying the fractions, the formula is y = 7/2 - (3/8)x

Slope-intercept form is y = mx + b, so the terms on the left side of the equation need to be rearranged for it to truly be in slope-intercept form:

y = -(3/8)x + 7/2

Be sure to keep the negative signs in front of their terms! (if you have any negative sings, there will be times when you won't.)

The equation of the line 3x + 8y = 28 in slope-intercept form is

y = -(3/8)x + 7/2. The slope of this line is -3/8 (see How to find slope if you are given the equation of a line in slope-intercept form, above).

Another, faster way is to use the formula -a/b. The slope of the line 3x + 8y = 28 is -3/8. (Remember, this only works for standard form (ax + by = c).)

Answer 2

y= 4/5 x - 8, find Slope