Connect the steps

Slope-intercept form: find y = mx + b

Use a slope and a point to find the intercept and line equation.

A nonvertical straight line can be written as y = mx + b. Here m is the slope and b is the y-intercept: the y coordinate where the line crosses the vertical axis, when x = 0.

From two points to one equation

Take A = (1, 2) and B = (5, 4). First calculate the slope: m = (4 − 2)/(5 − 1) = 1/2. Then substitute either point into b = y − mx. Using A gives b = 2 − (1/2) × 1 = 3/2.

Use B to verify the result: (1/2) × 5 + 3/2 = 5/2 + 3/2 = 4. Both points satisfy the equation, as they should.

Interpret the two numbers separately

The slope describes a rate of change. The intercept describes the value at x = 0. A line can have a positive slope and a negative intercept, or a negative slope and a positive intercept. The sign of b does not determine whether a line rises or falls.

Horizontal lines fit this form

For points (-2, 3) and (4, 3), the slope is 0. Substitution gives b = 3. The equation is y = 0x + 3, usually shortened to y = 3. Every x coordinate has the same y value.

Vertical lines do not

For (2, -1) and (2, 5), the equation is x = 2. There is no finite slope m that expresses this as y = mx + b. Depending on x, a vertical line has many y values rather than one, so it is not the graph of a function y of x.

Keep fractional coefficients unambiguous

Write y = (2/3)x − 1 when typing a fractional coefficient. Parentheses make it clear that the fraction multiplies x. The calculator keeps exact fractions in the equation, even when their decimals repeat.

For another useful arrangement, see point-slope form. For exceptions, read zero versus undefined slope. You can check both coordinates with the calculator.