Question

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select the graph of the line that passes through a(2, - 5), parallel to $overrightarrow{bc}$ with b(1, 3) and c(4, 5)

Explanation:

Step1: Find the slope of $\overrightarrow{BC}$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For points $B(1,3)$ and $C(4,5)$, we have $x_1 = 1,y_1 = 3,x_2=4,y_2 = 5$. Then $m_{BC}=\frac{5 - 3}{4 - 1}=\frac{2}{3}$.

Step2: Analyze the position of point $A(2,-5)$

Since the line we want is parallel to $\overrightarrow{BC}$, its slope $m$ is also $\frac{2}{3}$. A line with a positive slope rises from left - to - right. Point $A(2,-5)$ is in the fourth quadrant.

Step3: Check each option

Option A: The line has a negative slope.
Option B: The line has a negative slope.
Option C: The line passes through point $A(2,-5)$ and has a positive slope of $\frac{2}{3}$ (as it rises 2 units for every 3 units of run).
Option D: The line does not pass through point $A(2,-5)$.

Answer:

C