Question

question 16 of 25
what is the y-intercept of the line passing through the point (5,-6) with a slope of $-\frac{1}{7}$?

a. $-\frac{47}{7}$

b. $\frac{47}{7}$

c. $\frac{37}{7}$

d. $-\frac{37}{7}$

Explanation:

Step1: Recall the slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the $y$ - intercept. We know that $m=-\frac{1}{7}$, and the line passes through the point $(x,y)=(5, - 6)$.

Step2: Substitute the values into the equation

Substitute $x = 5$, $y=-6$ and $m =-\frac{1}{7}$ into the equation $y=mx + b$:

$$
LATEXBLOCK0
$$

Step3: Solve for $b$

To solve for $b$, we add $\frac{5}{7}$ to both sides of the equation:

$$
LATEXBLOCK1
$$

Answer:

D. $-\frac{37}{7}$