Question

The graph of a linear function f is shown. (a) Identify the slope, y-intercept, and x-intercept. (b) Write an equation that defines f.

Accepted Answer

Step 1: Identify the y-intercept by finding the point where the line crosses the y-axis. From the graph, the line crosses the y-axis at (0, 10), so the y-intercept is 10. Step 2: Identify the x-intercept by finding the point where the line crosses the x-axis. From the graph, the line crosses the x-axis at (5, 0), so the x-intercept is 5. Step 3: Calculate the slope of the line using the formula $$	ext{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2$ - y_1$}{x_2$ - x_1$}. $$Using the points (0, 10) and (5, 0), substitute to get $$\frac{0 - 10}{5 - 0} = \frac{-10}{5}. $$Step 4: Simplify the slope calculation to find the slope value. This will give you the slope of the line. Step 5: Write the equation of the line in slope-intercept form $$y = mx + b$$, where $$m is $$the slope and $$b is $$the y-intercept. Substitute the slope and y-intercept values found in previous steps to write the equation defining the function $$f.$$

The graph of a linear function f is shown. (a) Identify the slope, y-intercept, and x-intercept. (b) Write an equation that defines f.

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Key Concepts

Slope of a Linear Function

Intercepts of a Linear Function

Equation of a Line in Slope-Intercept Form