Match the equation of the line with the point it contains and its slope.
-$2 y - 9 x = 16$
A) $( - 1 , - 7 ) , ( - 8 , - 3 )$
B) $( - 6 , - 1 ) , ( - 4 , - 10 )$

Question

Match the equation of the line with the point it contains and its slope.
-$2 y - 9 x = 16$ 
A) $( - 1 , - 7 ) , ( - 8 , - 3 )$ 
B) $( - 6 , - 1 ) , ( - 4 , - 10 )$

Quizplus · Accepted Answer

To find the slope of the line we need to put it in slope-intercept form, which is  y = mx + b. We can rearrange the given equation to this form by solving for y:
\begin{align*}
2y-9x &= 16 \
2y &= 9x + 16 \
y &= \frac{9}{2}x + 8 
\end{align*}

Now we can see that the slope of the line is 9/2.

Next, we need to check which of the given points lie on this line. Let's check the points from choice (B):
\begin{align*}
(-6,-1) &: y =\frac{9}{2} \cdot (-6) + 8 = -13 \
(-4,-10) &: y =\frac{9}{2} \cdot (-4) + 8 = -10 
\end{align*}

We can see that the point (-4,-10) lies on the line, but the point (-6,-1) does not. Therefore, the best choice is (B).

Match the Equation of the Line with the Point It 2y−9x=162 y - 9 x = 162y−9x=16

Match the Equation of the Line with the Point It $2 y - 9 x = 16$