Question

the function g is defined by $g(x) = -3x - 42$. when graphed in the $xy$-plane, the graph of $y = g(x)$ intersects the $x$-axis at $(c, 0)$ and intersects the $y$-axis at $(0, d)$, where $c$ and $d$ are integer constants. what is the value of $\frac{d}{c}$?

a. -14
b. -3
c. 3
d. 14

Explanation:

Step1: Find c (x - intercept)

To find the x - intercept, set \(y = 0\) in \(y=-3x - 42\). So, \(0=-3x - 42\).
Add \(3x\) to both sides: \(3x=-42\).
Divide both sides by 3: \(x = c=-14\).

Step2: Find d (y - intercept)

To find the y - intercept, set \(x = 0\) in \(y=-3x - 42\). So, \(y=d=-3(0)-42=-42\).

Step3: Calculate \(\frac{d}{c}\)

Substitute \(c=-14\) and \(d = - 42\) into \(\frac{d}{c}\). We get \(\frac{-42}{-14}=3\).

Answer:

C. 3