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Function $A$ is a linear function whose graph includes the points $(0,-7)$ and $(3,0)$ . $\newline$ Which of the following functions has the same $y$ -intercept as Function $A$ ? $\newline$ Choices: $\newline$ (A) $y = -7$ $\newline$ (B) $y = -\frac{7}{3}x$ $\newline$ (C) $y = 3$ $\newline$ (D) $y = \frac{7}{3}x$

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Write equations of cosine functions using properties

Full solution

Q. Function

A

is a linear function whose graph includes the points

(0,-7)

and

(3,0)

.

\newline

Which of the following functions has the same

y

-intercept as Function

A

?

\newline

Choices:

\newline

(A)

y = -7

\newline

(B)

y = -\frac{7}{3}x

\newline

(C)

y = 3

\newline

(D)

y = \frac{7}{3}x

Find Slope of Function A: Find the slope of Function A using the points $(0,-7)$ and $(3,0)$ . Slope $m$ = $\frac{y_2 - y_1}{x_2 - x_1}$ = $\frac{0 - (-7)}{3 - 0}$ = $\frac{7}{3}$ .
Write Equation of Function A: Write the equation of Function A using the slope and y-intercept. $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. Since the y-intercept is given as $(0,-7)$ , $b = -7$ . So, the equation is $y = \frac{7}{3}x - 7$ .
Compare Y-Intercept: Compare the $y$ -intercept of Function $A$ with the given choices. The $y$ -intercept of Function $A$ is $-7$ , so we are looking for a function with the same $y$ -intercept.
Choice (A) Analysis: Choice (A) $y = -7$ is a horizontal line with a $y$ -intercept of $-7$ , which matches the $y$ -intercept of Function A.

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