Put Into Slope-Intercept Form Calculator

Use this put-into-slope-intercept-form calculator to rewrite a linear equation as y = mx + b. Enter the coefficients of an equation in standard form, Ax + By = C, and it returns the slope and y-intercept along with the rearranged equation.

Formula

The calculator starts with the standard-form equation Ax + By = C, then isolates y:

By = -Ax + C, so y = (-A/B)x + C/B.

Here, A is the coefficient of x, B is the coefficient of y, and C is the constant on the right side. The slope is m = -A/B, and the y-intercept is b = C/B. These are pure numbers in the equation; their physical units, if any, depend on what the variables represent.

Important: The calculator block’s output specification must express the requested equation using supported numeric expressions, but a slope-intercept equation contains both a slope and an intercept and is not a single numeric quantity. In the example specification, the output expression is consequently not capable of displaying the equation as written; it evaluates only a number. Use the algebraic formula above, or a calculator that supports symbolic equation output, to obtain the full rearranged equation.

Worked Example

Using the block’s default inputs, the equation is 2x + 3y = 6. Isolate y step by step:

1. Subtract 2x from both sides: 3y = -2x + 6.
2. Divide every term by 3: y = (-2/3)x + 2.
3. Read off the slope, m = -2/3, and the y-intercept, b = 2.

The result is y = (-2/3)x + 2. This worked result follows the rearrangement formula. The numeric-only output line in the block does not return this complete equation, so it should not be mistaken for a functioning symbolic calculator result.

What Slope-Intercept Form Means

Slope-intercept form is a way to write a straight-line relationship as y = mx + b. The slope m describes how much y changes when x increases by one unit. The intercept b is the value of y when x = 0, so the line crosses the y-axis at (0, b).

For example, in y = 4x – 3, the slope is 4 and the y-intercept is -3, or the point (0, -3). A positive slope rises from left to right; a negative slope falls. A zero slope gives a horizontal line, such as y = 5.

How to Put an Equation Into This Form

When an equation is given as Ax + By = C, the reliable method is to isolate the term containing y first, then divide by its coefficient. Apply each operation to both sides to preserve equality.

• Move the x-term and constant as needed so the y-term is alone on one side.
• Divide every term by the coefficient of y.
• Write the result in the order y = mx + b.
• Check by substituting a point from the original equation into the rearranged one.

For 4x – 2y = 8, subtract 4x to get -2y = -4x + 8. Divide by -2: y = 2x – 4. The negative divisor changes both signs, which is a frequent source of errors.

When This Form Is Useful

Slope-intercept form makes the line’s rate of change and starting value visible without further rearrangement. It is especially handy for graphing: plot (0, b), then use the slope as a rise-over-run step to find another point. A slope of 2/3, for instance, means moving 3 units right and 2 units up; a slope of -2/3 means moving 3 right and 2 down.

It is also useful for comparing linear relationships. If two equations have the same slope but different intercepts, their graphs are parallel. If their slopes differ, they generally meet at one point. The form appears in contexts such as constant-rate costs and distance-versus-time models, provided the variables and units are interpreted correctly.

Common Problems and Limits

• Dividing by zero: If B = 0, the equation has no y-term and cannot be put into ordinary slope-intercept form. For example, 2x = 6 is the vertical line x = 3, whose slope is undefined.
• Sign errors: Moving a term across the equals sign changes its sign. Dividing by a negative coefficient changes the signs of all terms.
• Confusing the intercepts: In y = mx + b, b is the y-intercept. It is not automatically the x-intercept, which is found by setting y = 0.
• Rounding too early: Keep fractions exact while rearranging, then convert to decimals only if useful. A rounded slope may give slightly different plotted points.

A vertical line cannot be represented as y = mx + b. Other linear forms may also require additional algebra before they fit this pattern. Moreover, a numerical equation alone does not explain the meaning of its slope or intercept; that depends on the definitions and units of x and y.

Frequently Asked Questions

How do I convert Ax + By = C to slope-intercept form?
Subtract Ax from both sides and divide by B: y = (-A/B)x + C/B, as long as B is not zero.

What is the slope in y = mx + b?
The slope is m, the coefficient multiplying x. It represents the change in y for each one-unit increase in x.

What is the y-intercept?
The y-intercept is b, the value of y when x = 0. The line crosses the y-axis at (0, b).

Can every line be written in slope-intercept form?
No. Vertical lines, written x = k, have undefined slope and cannot be expressed as y = mx + b.

How do I check my rearranged equation?
Substitute a point that satisfies the original equation into the new one. If it satisfies both equations, that is a useful check; you can also reverse the algebra to recover the original form.

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in A | x coefficient A | - | 2 | 0
in B | y coefficient B | - | 3 | 0
in C | constant C | - | 6
out equation | Slope-intercept equation | - | (C - A * 0) / B | 0