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.

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.

If it's a straight line, choose any two points on the graph and use the formula m = (y2 - y1)/(x2 - x1) to find the slope. For example, if point A has the coordinates (2, 8) and point B has the coordinates (7, 15): (15 - 8)/(7 - 2) = 7/5, therefore the slope of the line which connects A and B would be 7/5.

If you only have a single coordinate, it is not possible to find the slope of the line - you need to know at least two points on the line to find the slope.

Use the slope-intercept form of the equation: y = mx + b, where m is the given slope, and b is the given y-intercept. For example, if the given slope is 2, and the given y-intercept is -4, the equation will be y = 2x - 4. Then make a table of values, choosing small positive and negative values for x and calculating the corresponding values of y. Now plot the points you've found, and connect them with a line.

First solve for y: x - 3y - 6 = 0. -3y = 6 - x. y = (x-6) / 3 = x/3 - 2. So y = (1/3)x - 2. That's in slope-intercept form, so the slope of the line is the coefficient of x, which is +1/3.

This line's equation is given in the "slope-intercept" form, y = mx + b, where "m" is the slope, and "b" is the y-intercept. Therefore, the slope is given to us as -5.

The slope is (5-2)/(3-5) = 3/-2 = -3/2.

The vertical change (in y) is the numerator of the slope, and the horizontal change (in x) is the denominator. (If the slope is a whole number, that number can be considered the numerator, and the denominator is 1.)

Using the slope-intercept formula, y = mx + b, the slope (m) in this case is 3, and the y-intercept (b) is zero. (A slope of 3 means that the line moves up three times faster than it moves to the right -- or down three times faster than it moves to the left.)

Choose two random points on the line. It is easiest if they are on a point where the x and y lines intersect. Pick and label which one is "point one" and "point two." Subtract y coordinate one from y coordinate two (y2 - y1) and put it as the numerator in a fraction. Do the same with the x coordinates, but put the difference as the denominator. Put the completed fraction into decimal form. A line going from left to right down will have a negative slope, and a line going up to the right will have a positive slope.