Find the slope and y-intercept of y = 3x − 4.
Incorrect answer: Slope −4; y-intercept (0, 3)
The intercept b is not an x-coordinate. A vertical line x = c cannot be written as y = mx + b, because its slope would require division by zero.
Swapping slope and intercept
The coefficient of x is the rate of change; the constant is the output when x is zero.
The correction
Slope 3; y-intercept (0, −4)
Match the coefficient and constant to y = mx + b.
- If necessary, rearrange the equation to isolate y.
- Find slope using change in y divided by change in x, keeping the point order consistent.
- Use x = 0 to identify b, or substitute a known point into y = mx + b. Plot the intercept and use the slope to locate another point.
Try the reasoning in another example
Write 2x + y = 7 in slope-intercept form.
- Subtract 2x from both sides.
- The resulting equation directly shows the coefficient of x and the constant.
Answer: y = −2x + 7
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