Question

The graph of linear function k passes through the points (-8, -4) and (7, 8).

Select the statement(s) that must be true. More than one statement may be selected.
A. The graph of k passes through the point (3, 0).
B. The x-intercept of the graph of k is -3.
C. The slope of k is 4/5
D. The zero of k is -3.

Answer 1

The graph of function k has a slope of 4/5, which makes statement C correct. Statements B and D are also correct as the x-intercept and zero of the function are -3. Statement A is incorrect because the line does not pass through (3, 0).

Step-by-step explanation:

The student is asking about the properties of a linear function that passes through two given points (-8, -4) and (7, 8). To determine the statements that must be true, we first need to calculate the slope of the line (m) using the formula m = (y2 - y1) / (x2 - x1).

Using the given points, the slope is calculated as m = (8 - (-4)) / (7 - (-8)) = 12/15 = 4/5, which means statement C is correct.

To find the x-intercept, we set y to 0 in the linear equation derived from the slope and a point.

Using point-slope form y - y1 = m(x - x1) and plugging in a known point (-8, -4) and the slope 4/5, we get y - (-4) = 4/5(x - (-8)). We then find x when y = 0 which is x = -3.

Hence, statement B and D are correct as they both refer to the x-intercept (also known as the zero of the function).

Statement A is incorrect as substituting x = 3 in the equation does not result in y = 0, it instead gives a different value for y.