Question

Miguel wrote two equations. he thinks the two equations represent parallel lines. is he correct? explain why or why not.

Answer 1

Answer:

Yes, he is correct because both the lines have same slope.

Step-by-step explanation:

Given:

The two equations are:

$-2x+6y=-42\\y+10=\frac{1}{3}(x-3)$

Two lines are parallel only if their slopes are equal.

So, let us write each equation in slope-intercept form $y=mx + b$, where, $m$ is the slope of the line.

Equation 1 is:

$-2x+6y=-42\\6y=2x-42\\y=\frac{2}{6}x-\frac{42}{6}\\y=\frac{1}{3}x-7$

So, the slope of line 1 is $m_{1}=\frac{1}{3}$

Now, equation 2 is:

$y+10=\frac{1}{3}(x-3)\\y+10=\frac{1}{3}x-3\times \frac{1}{3}\\y+10=\frac{1}{3}x-1\\y=\frac{1}{3}x-1-10\\y=\frac{1}{3}x-11$

Therefore, slope of line 2 is, $m_{2}=\frac{1}{3}$

∵ $m_{1}=m_{2}=\frac{1}{3}$

Therefore, both the lines are parallel to each other.