Question

The graph of linear function k passes through the points(-7,0) and (1,8). Which statement must be true

Answer 1

Answer:

✅The x-intercept of the graph of k is -7.

Step-by-sep explanation:

Graph the equation of the line that passes through the points, (-7, 0) and (1, 8) by first generating an equation, and then using the equation of the function to plot the graph.

To find the equation, we need to calculate the slope, m, and y-intercept, b.

✅Using points (-7, 0) and (1, 8), the slope of the line is:

$m = \frac{y_2 - y_1}{x_2 -x_1} = \frac{8 - 0}{1 -(-7)} = \frac{8}{8} = 1$

Substitute x = 1, y = 8, m = 1 into $f(x) = mx + b$ to find the y-intercept, b, of the function. (Note: f(x) is same as variable y).

$8 = 1(1) + b$

$8 = 1 + b$

Subtract 1 from each side

$8 - 1 = b$

$7 = b$

$b = 7$

Substitute m = 1 and b = 7 into $f(x) = mx + b$

The equation of the function is:

$f(x) = (1)x + 7$

$f(x) = x + 7$

The graph of the function, k, is shown in the attachment below.

❌Now, we know that the slope of the function, m, is 1. Therefore, option A is not correct.

We also know that the graph of the function, k, does not pass through the points (-1, -8). We can confirm this looking at the graph. ❌The point (-1, -8) is not on the line of the graph. Therefore, option B is not correct.

❌The zero of k, is the value of x for which the function, f(x) or y = 0. From our graph, y = 0, when x = -7. This can also be referred to as the x-intercept. The zero of k is -7, not 7.

Therefore, option C is not correct.

✅The x-intercept is where the line of the function of intercepts the x-axis. From our graph, the line intercepts the x-axis at x = -7.

So, the x-intercept of the graph of k is -7.

Therefore, option D is the only statement that is TRUE.