In slope-intercept form y = mx + b, the y-intercept is b — the constant term. Here b = −4, so the line crosses the y-axis at (0, −4). The value 3 is the slope, not the intercept. A common error is reading the coefficient of x as the intercept or dropping the negative sign.
Question 2 True / False
The graph of the equation y = 5 is a vertical line.
TTrue
FFalse
Answer: False
y = 5 means 'y is always 5, no matter what x is.' Every point on this line has y-coordinate 5, so the line runs horizontally across the plane. Vertical lines are described by x = constant (e.g., x = 5). Confusing horizontal and vertical is one of the most common graphing errors.
Question 3 Short Answer
You are graphing y = (3/4)x + 2 using the slope-intercept method. After plotting the y-intercept, describe exactly how you would use the slope to find the next point.
Think about your answer, then reveal below.
Model answer: Plot the y-intercept at (0, 2). Then move right 4 units (run) and up 3 units (rise) to land on the next point at (4, 5).
Slope = rise/run = 3/4. Starting at the y-intercept (0, 2), move in the direction that rise/run describes: 3 up and 4 to the right. This gives (0+4, 2+3) = (4, 5). Many students try to plot slope as a single coordinate rather than as a directed movement.