Question

question 7 of 10, step 2 of 2
consider the following relation.
-4x - 7y = 5
step 2 of 2: determine if the relation is a function. if it is not, identify two ordered pairs as proof.
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Explanation:

Step1: Rewrite in slope-intercept form

Rearrange the equation to solve for $y$:
$$-4x -7y = 5$$
$$-7y = 4x + 5$$
$$y = -\frac{4}{7}x - \frac{5}{7}$$

Step2: Apply Vertical Line Test

A linear equation in this form (non-vertical line) passes the vertical line test: any vertical line intersects the graph at most once. For any input $x$, there is exactly one output $y$.

Answer:

This relation is a function. The equation represents a non-vertical straight line, which passes the vertical line test, meaning every $x$-value has exactly one corresponding $y$-value.