Short answer
Slope-intercept form is y = mx + b, where m is slope and b is the y-intercept. Rearranging other linear equations into this form makes graphing and interpretation faster.
- m tells how fast y changes per unit of x.
- b gives the output when x equals zero.
- Rewriting equations into y = mx + b reveals slope direction immediately.
Convert from standard form
Standard form often appears as Ax + By = C. Solve for y to expose slope and intercept. Keep fraction slopes exact until the final step to avoid rounding drift.
If B is negative, watch sign changes when dividing both sides by B.
Interpret in context
In budgeting, m can represent dollars per month while b is the initial balance. In population models over short periods, m is average net change per time unit and b is the starting count.
- Positive m means increasing trend.
- Negative m means decreasing trend.
- b is meaningful only when x = 0 is in the context range.
Rewrite and interpret a linear equation
A gym tracks calories burned with equation 3x - 2y = -10, where x is minutes and y is calories in tens.
- Isolate y: -2y = -3x - 10.
- Divide by -2: y = (3/2)x + 5.
- Read slope and intercept: slope is 1.5, intercept is 5.
- Interpret: at 0 minutes, model predicts 50 calories (since y is tens).
Result: Slope-intercept form is y = (3/2)x + 5, with positive growth rate.
Common mistakes
- Changing signs incorrectly while isolating y.
- Treating b as x-intercept instead of y-intercept.
- Rounding slope too early and altering later results.
- Ignoring units when interpreting m and b.
Try one
Write 2x + y = 7 in slope-intercept form.
Subtract 2x from both sides: y = -2x + 7.
Sources
- OpenStax: College AlgebraOpen textbook with full chapter coverage, worked examples, and practice problems.
- Khan Academy: Algebra and Algebra 2Official lessons and practice sets for core algebra skills.