Q&A for How to Calculate Slope and Intercepts of a Line

Use the formula y = mx + b, where m is the slope and b is the y-intercept.

Assuming you're talking about a linear (straight-line) equation, you would use the standard slope/y-intercept form, y = mx + b. Use the given slope for m, the coefficient of x. Use the given y-intercept for b, the constant in the equation. For example, if the slope is 3 and the y-intercept is -5, the equation would be y = mx + b = 3x + (-5) = 3x - 5.

There are two types of intercept, x-intercept and y-intercept. When we say x-intercept, this means the line passes through the x-axis with coordinates (x,0). When we say y-intercept, the graph passes through the y-axis with coordinates (0,y). To find x or y intercepts, just observe where the line on the graph cuts the x or y axis respectively.

That is a graph showing more than one function, equation, or line.

The standard equation is y = mx + b, where m is the slope, and b is the y-intercept. The slope is given as 4. Thus, y = 4x + b. The point (-2,-4) fits into the equation, so we can insert those x and y values into the equation. Thus, -4 = 4(-2) + b = -8 + b. Adding 8 to both sides of the equation results in 4 = b. Thus, the equation we're looking for is y = mx + b = 4x + 4.

With two points, (0,5) and (-5,0), you can compute slope directly by dy/dx. The slope = dy/dx = (5-0)/(0-(-5))= 1.

You are given two points: (-3/4, 0) and (-2, 1/3). Slope is defined as rise over run or delta y over delta x, so plug the known coordinates into that formula. Slope = (0 - 1/3) / (-3/4 - (-2)) = (-1/3) / (5/4) = -4/15.

The y-intercept occurs when x=0. So substitute 0 for x in the equation, and solve for y. y = 2(x-1)² + 5. Substituting 0 for x: y = 2(0-1)² + 5 = 2(-1)² + 5 = 2(1) + 5 = 2 + 5 = 7. So y is 7 when x is 0, and the y-intercept is 7.

Take the maximum quantity to be represented on either axis, and divide it by the number of units available on that axis. The quotient will be the quantity to be represented by each unit. This can be done separately for each axis, although typically a single scale is used for both axes.

X is the sideways line, y is the upwards/downward line. Namely, x is vertical, y is horizontal.

If the line never crosses the Y axis, there isn't a Y intercept, so it's not possible to find this. There are plenty of functions that don't intercept the Y intercept, so don't worry if you can't find it.

To work out the slope of the line, you can rearrange the function into the form y=mx+c. In your example, this would be rearranged as by=c-ax -> y=(c-ax)/b -> y = (c/b)-(a/b)x. Therefore, the slope of your line would be -(a/b).

To find the y-intercept, substitute x with 0. If the function of the line was y=7x+5: y=7(0)+5 -> y= 0+5 -> y=5, therefore, the line intercepts y at the point (0,5).

To calculate the gradient of a line between two points, you can use the formula m = (y2 - y1)/(x2-x1). In your example: m = (-3 - 5)/(7 - 9) -> m = (-8)/(-2) -> m = 4.

Change the equation into the slope-intercept form (y = mx + b). First subtract 5x from both sides: -2y = -5x + 20. Then divide both sides by -2: y = 5/2x - 10. That's the slope-intercept form. That means m = 5/2, which is the slope.