Q&A for How to Find the Slope of a Line

Re-work the equation until y is isolated on one side. Then note the coefficient of the x term. That's the slope. In this example, we re-work the equation until we isolate y: y = x/2 - 5. The coefficient of x is ½, so the slope of the line is ½.

For all lines where y equals a constant and there is no x, the slope is 0.

The slope of a line is a non-angular representation of the angle between the line and a horizontal line such as the x-axis. Use a protractor to measure that angle, and then convert the angle to a decimal or a fraction using a trig table. For example, if a protractor tells you that there is a 45° angle between the line and a horizontal line, a trig table will tell you that the tangent of 45° is 1, which is the line's slope. Most angles do not have such a simple tangent. For instance, a 30° angle has a tangent of 0.577. You could use that as the slope, or you could convert the decimal to a fraction, but in this case it would be a rather unwieldy fraction (577/1000 or 72/125).

You're describing a curved line. Each point on a curve has its own unique slope, so the curve (or function) as a whole does not have a specific slope.

The slope is the change in y divided by the change in x. The change in y is (-4) - (-5) = -4 + 5 = +1. The change in x is (-6) - (+5) = -6 - 5 = -11. So the slope is +1 / -11 = -1/11. (A negative slope means the line moves down as it moves from left to right, and this slope is just slightly negative.)

No. Since the line increases at a constant rate, the ratio of (y2-y1)/(x2-x1) will stay the same.

Answer is -5/4. You take 8 as your y2 and -7 as your x2. With the rest following in that order, you will be able to get -15/12 which is equal to -5/4.

You would have to use a protractor and trigonometry.

A straight line with a slope of -1 moves down at a 45° angle as it moves to the right.

When you are given a slope-intercept form equation, then finding the slope is simple: since the slope-intercept form is y = mx + b, and m = slope, it would simply be the coefficient of x. For example, if the question were, "Find the slope when the equation is y = 5x + 2", the slope would be 5, because that is where the slope goes in a slope-intercept form.

The method shown above works with any straight line on a coordinate plane. The line does not have to pass through any particular point. Note that the line in the images above does not pass through (0,0).

It's usually best to simplify any answer. In this case the slope is 1.25 or 1¼. (An unsimplified fraction such as 5/4 is also an acceptable answer when you're dealing with slope.)

Presumably you would have an equation representing the line. If the equation is not already expressed in the form "y = mx + b", arrange it in that form. m will be the slope. (This is for straight-line graphs only.)

Yes, "slope" is also referred to as "gradient."

We'll designate 8 as y2 and 3 as x2. Then 5 is y1 and 0 is x1. So the slope is (8 - 5) / (3 - 0) = 3/3 = 1.

Isolate y. Subtract 2x on both sides. -4y = -2x + 20. (y = mx + b form). Then divide by -4 on both sides. y = 1/2x - 5. The number in front of the x is 1/2, so that's your slope.

The slope is going to be -3/2. The equation will be -2y = 3x + b, so y = -3/2x + b/2. We don't know what b is, but it doesn't matter.

Isolate y in the equation. Just make sure the equation is in y = mx + b form for this. The unit inside the "m" portion is your slope.

When the y value is just a constant, that number becomes a point. It has no run and no rise. As in this case when the y equals a constant, the slope is equal to zero. So the slope is 0.

See the wikiHow article How to Find the Equation of a Line for further information.

Subtract 2x on both sides. 5y = -2x + 2. Then divide by 5 on both sides. y = -2/5x + 2/5. This is in y = mx + b form where m is the slope. Therefore, your slope, m, is -2/5.

The slope is (y2 - y1) / (x2 - x1). (1 - 2) / (6 - 4) = -1 / 2.

m is the slope of the line. The slope is the amount of change in the y-value of the line as its x-value changes.

Subtracting a negative number is the same as adding a positive number. For example, if y2 is 4, and y1 is -2, when you subtract y1 from y2, you get 4 - (-2) = 4 + 2 = 6. Another example: if y2 is -5, and y1 is -3, when you subtract y1 from y2, you get -5 - (-3) = -5 + 3 = -2. In each case, you are looking for the "distance" between y2 and y1 or between x2 and x1. For example, the "distance" (number of units on a number line) between +1 and -5 is 1 - (-5) = 1 + 5 = 6.

First change the equation into the standard form (y = mx + b), where m is the slope. Thus, we solve for y. Do this by adding x to both sides (so that -4y = x + 12) and then dividing both sides by (-4): that gives you y = -x/4 - 3. Now that the equation is in standard form, we can see that "m" (the coefficient of x) is -1/4. That's the slope.

First recognize that the slope-intercept form applies only to linear (straight-line) equations, those that have no exponents other than 1. Manipulate the equation until it takes the form of y = mx + b. For example, if the equation is 4x + 2y = 8, you would subtract 4x from both sides of the equation and then divide both sides by 2. That results in the equation y = -4x + 8. That's the slope-intercept form. Be aware that both m and b can be either positive or negative, and they can be whole numbers or fractions.

The slope is 3. This is in y = mx + b form. m is the slope and b (-2) is the y-intercept.

y = mx + b is the "slope-intercept form". m = y2-y1/x2-x1 is one way to find the slope when you're given two points. y - y1 = m(x-x1) is known as the "point-slope form".

Solve for y. First subtract 5 from both sides: 4x - 5 = 7y. Then divide both sides by 7: y = 4/7x - 5/7 = y. The number in front of x is 4/7, so that's the slope.

Because those two points have the same x-coordinate, the line is vertical (parallel to the y-axis). That makes the slope infinite or undefined, so it cannot be stated.