Question

the graph of a linear function f is shown a. identify the slope, y-intercept, and x-intercept. b. write the equation that defines f. the slope is -4. (type an integer or a simplified fraction.) the y-intercept is (type an ordered pair.)

Explanation:

Step1: Recall y-intercept definition

The y-intercept is the point where the line crosses the y-axis, so \( x = 0 \).

Step2: Identify the point from the graph

From the graph, the line crosses the y-axis at \( (0, 9) \)? Wait, no, looking at the grid, when \( x = 0 \), the y - value is 9? Wait, no, let's check again. Wait, the graph: when x=0, the line is at y=9? Wait, no, the grid: the y-axis is at x=0. Looking at the graph, the line intersects the y-axis at (0, 9)? Wait, no, maybe I misread. Wait, the graph: the line goes through (0, 9)? Wait, no, let's check the coordinates. Wait, the y-intercept is the point where x=0. From the graph, when x=0, the y-coordinate is 9? Wait, no, looking at the grid, the vertical axis is y, horizontal is x. At x=0, the line is at y=9? Wait, no, maybe (0, 9) is wrong. Wait, let's see the graph again. Wait, the line passes through (0, 9)? Wait, no, the user's graph: the y-axis is at x=0, and the line crosses the y-axis at (0, 9)? Wait, no, maybe (0, 9) is incorrect. Wait, let's check the slope is -4. Let's use the slope-intercept form \( y = mx + b \), where m is slope, b is y-intercept (the y-value when x=0). Wait, from the graph, when x=0, the y-coordinate is 9? Wait, no, looking at the grid, the y-axis has marks at 10, 8, 6, 4, 2, 0, -2, etc. Wait, the line crosses the y-axis at (0, 9)? Wait, no, maybe (0, 9) is wrong. Wait, maybe (0, 9) is correct? Wait, no, let's check the x-intercept: when y=0, x= 9/4? No, wait, the x-intercept is (2.25, 0)? No, the graph shows the line crosses the x-axis at (2, 0)? Wait, no, the x-intercept is where y=0. From the graph, the line crosses the x-axis at (2, 0)? Wait, no, let's calculate. If slope is -4, and y-intercept is (0, b), then the equation is \( y = -4x + b \). When x=2, y=0 (from the graph, the line crosses x-axis at (2, 0)). So plug in x=2, y=0: \( 0 = -4(2) + b \) → \( 0 = -8 + b \) → \( b = 8 \). Wait, so y-intercept is (0, 8). Oh! I made a mistake earlier. So the y-intercept is (0, 8) because when x=0, y=8 (from the graph, the line crosses the y-axis at (0, 8)). Let's verify: slope is -4, so from (0, 8), moving 1 unit right (x=1), y should be 8 - 4 = 4. Does the graph have (1, 4)? Let's check the grid. At x=1, y=4? Yes, that seems right. Then x=2, y=0, which matches the x-intercept. So the y-intercept is (0, 8).

Answer:

(0, 8)