Graphing a linear equation from standard form

Intercepts come from setting one coordinate to zero

At the x-intercept, y is zero. At the y-intercept, x is zero. Substituting those values often creates two points with almost no algebra.

This route is especially efficient when both intercepts are integers. It is less useful when one coefficient is zero or the intercepts are awkward fractions.

Slope-intercept form reveals direction

Solving for y turns standard form into y = mx + b, where m controls the step pattern and b gives a starting point.

Use legal equation moves on every term. Dividing by B means dividing the x-term, the constant, and their signs by B.

A graph needs a check, not just two dots

Substitute a plotted point into the original equation. A point that misses the equation exposes an arithmetic or plotting error immediately.

Vertical lines have the form x = constant and cannot be written as y = mx + b. Horizontal lines have slope zero and the form y = constant.

Worked example

Common mistakes

• Setting x and y to zero at the same time.
• Dividing only part of the equation when solving for y.
• Trying to assign a finite slope to a vertical line.

Keep these ideas

• Intercepts are coordinate-zero points.
• Standard and slope-intercept forms describe the same line.
• Check a plotted point in the original equation.