In the xy-plane, the graph of y = f(x) is a line that passes through (0, 27) and has a slope of 5. Which equation defines f?

In the xy-plane, the graph of y = f(x) is a line that passes through (0, 27) and has a... | SAT Linear functions Practice

Answer: D. $f(x)=5x+27$

Explanation:1. Recall the slope-intercept form of a linear equation: The slope-intercept form is $y = mx + b$ or $f(x) = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

Identify the given slope and y-intercept: The slope of the line is given as $m = 5$ . The line passes through the point $(0,27)$ . When a line passes through a point $(0,b)$ , $b$ is the y-intercept. So, the y-intercept is $b = 27$ .
Substitute the slope and y-intercept into the slope-intercept form: $f(x) = mx + b$ $f(x) = 5x + 27$
Check the solution with the options: The equation we derived is $f(x)=5x+27$ . This matches option [D].
Conclusion: The equation that defines f is $f(x)=5x+27$ .

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