Standard Form to Slope Intercept Calculator

The standard form of a linear equation is Ax + By = C (or sometimes written as Ax + By + C = 0), where A, B, and C are constants. This form is commonly used when solving systems of equations or when integer coefficients are preferred.

Slope-intercept form is y = mx + b. Here, m is the slope — it describes how steep the line is (rise over run). The value b is the y-intercept — the point where the line crosses the vertical (y) axis when x = 0.

Starting from Ax + By = C, isolate y by subtracting Ax from both sides to get By = -Ax + C, then divide everything by B: y = -(A/B)x + C/B. So the slope m = -A/B and the y-intercept b = C/B.

No. If B = 0 in the standard form equation, you cannot divide by B, meaning the line is vertical (e.g. x = 3). Vertical lines have an undefined slope and cannot be expressed in slope-intercept form y = mx + b.

Here A = 1, B = 1, C = 0. Applying the formula: slope m = -1/1 = -1 and y-intercept b = 0/1 = 0. So the slope-intercept form is y = -x, or equivalently y = -1x + 0.

Starting from y = mx + b, move the mx term to the left side: -mx + y = b. Multiply through by -1 if needed to make the x coefficient positive: mx - y = -b. Adjust to get integer coefficients if required.

No, they are different. Slope-intercept form is y = mx + b, which directly shows the slope and y-intercept. Point-slope form is y - y₁ = m(x - x₁), which uses a known point on the line and the slope. Both describe a line, but in different ways.

The slope (m) measures the rate of change — how much y increases or decreases for every 1-unit increase in x. The y-intercept (b) is a fixed point — specifically where the line hits the y-axis (where x = 0). Together they fully define a non-vertical straight line.