Question

(02.05 mc) the linear function f(x) is represented in the graph, and the linear function g(x) is represented in the table. which of the following best compares the slopes and y - intercepts of the two functions? (1 point) the slope of f(x) is greater than the slope of g(x). the y - intercept of f(x) is equal to the y - intercept of g(x). the slope of f(x) is greater than the slope of g(x). the y - intercept of f(x) is greater than the y - intercept of g(x). the slope of f(x) is equal to the slope of g(x). the y - intercept of f(x) is less than the y - intercept of g(x). the slope of f(x) is equal to the slope of g(x). the y - intercept of f(x) is greater than the y - intercept of g(x).

Explanation:

Step1: Find slope of f(x)

Using two - points on f(x) like (0, 2) and (4, 4), slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, so $m_f=\frac{4 - 2}{4-0}=\frac{2}{4}=\frac{1}{2}$

Step2: Find y - intercept of f(x)

The graph of f(x) intersects y - axis at y = 2, so $b_f=2$

Step3: Find slope of g(x)

Using two points from the table of g(x) like (-4,-1) and (-2,0), $m=\frac{y_2 - y_1}{x_2 - x_1}$, so $m_g=\frac{0+1}{-2 + 4}=\frac{1}{2}$

Step4: Find y - intercept of g(x)

When x = 0 in the table of g(x), g(x)=1, so $b_g = 1$

Answer:

The slope of f(x) is equal to the slope of g(x). The y - intercept of f(x) is greater than the y - intercept of g(x).