Question

Which of the following is a true statement about the linear function below.

the slope is 5
the x-intercept is (0, 10)
the y-intercept is (0, 4)
the equation is 5x + 2y = 20
a) All of the above
b) II and III only
c) I, II, and IV only
d) I and III only

Answer 1

The linear function has a y-intercept of (0, 4) and the equation 5x + 2y = 20. The true statements about the linear function are that the x-intercept is not (0, 10).

Step-by-step explanation:

The linear function in question can be represented by the equation 5x + 2y = 20. To determine which of the given statements are true, we can analyze each of them:

1. The slope of the linear function is 5. This is not correct, since the equation is in the form of 5x + 2y = 20, and the coefficient of x is 5, not the slope.
2. The x-intercept is (0, 10). This is also not correct. To find the x-intercept, we set y = 0 in the equation and solve for x. In this case, when we substitute y = 0 into the equation, we get 5x = 20, which gives us x = 4. Therefore, the x-intercept is (4, 0) and not (0, 10).
3. The y-intercept is (0, 4). This statement is correct. To find the y-intercept, we set x = 0 in the equation and solve for y. When we substitute x = 0 into the equation, we get 2y = 20, which gives us y = 10. Therefore, the y-intercept is (0, 10), which matches the given statement.
4. The equation of the linear function is 5x + 2y = 20. This statement is correct, as it matches the given equation.

Based on the analysis above, the true statements about the linear function are II and III only. Therefore, the correct answer is option b) II and III only.