Question

When a student sets (y = 0) into a linear equation, she can solve for (x) and gets (x = – 3). When she sets (x = 0) and solves the equation, she gets (y = 4). Which of the following is the correct statement of the intercepts and graph?

a) x-intercept: (0, -3), y-intercept: (4, 0)
b) x-intercept: (-3, 0), y-intercept: (0, 4)
c) x-intercept: (0, 4), y-intercept: (-3, 0)
d) x-intercept: (4, 0), y-intercept: (0, -3)

Answer 1

The correct statement of the intercepts for a linear equation of the form y = mx + b is option b: x-intercept: (-3, 0), y-intercept: (0, 4), as the x-intercept is where the line crosses the x-axis when y is zero, and the y-intercept is where it crosses the y-axis when x is zero.

Step-by-step explanation:

When interpreting the x-intercept and y-intercept of a linear equation, it’s important to know that for the equation y = mx + b, where m represents the slope and b represents the y-intercept, the x-intercept is when y equals zero and the y-intercept is when x equals zero. In the question posed, setting y to zero gives us an x-value of – 3, and setting x to zero gives a y-value of 4. Hence, the correct statement of the intercepts and the graph would be: x-intercept: (– 3, 0), y-intercept: (0, 4), which matches option b.