Question

multiple choice. choose the one alternative that best completes the statement or answers the question. find an equation of the line containing the given pair of points. write your final answer in slope - intercept form. 36) (-6,0) and (5,3) a) y = \frac{6}{11}x+\frac{18}{11} b) y = \frac{3}{11}x+\frac{18}{11} c) y=-\frac{6}{11}x+\frac{18}{11} d) y=-\frac{3}{11}x+\frac{18}{11}

Explanation:

Step1: Calculate the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1=-6,y_1 = 0,x_2=5,y_2 = 3$. So $m=\frac{3-0}{5 - (-6)}=\frac{3}{11}$.

Step2: Find the y - intercept

Use the point - slope form $y - y_1=m(x - x_1)$ and then convert to slope - intercept form $y=mx + b$. Using the point $(-6,0)$ and $m=\frac{3}{11}$, we have $y-0=\frac{3}{11}(x + 6)$. Expanding gives $y=\frac{3}{11}x+\frac{18}{11}$.

Answer:

B. $y=\frac{3}{11}x+\frac{18}{11}$