Question

Decide whether the graphs of the two equations are parallel lines. Explain your answer. $$ 2 x-12=y, y=10+2 x $$

Short answer

Yes, the graphs of the two given equations form parallel lines because they have the same slope.

Step-by-step solution

Rearrange Equation 1 Into Slope-Intercept Form

Rewrite the first equation, \(2x - 12 = y\), in slope-intercept form. This is done by switching the sides, resulting in the equation \(y = 2x - 12\).

Rearrange Equation 2 Into Slope-Intercept Form

The second equation, \(y = 10 + 2x\), should also be written in slope-intercept form. This can be achieved by reordering the terms, resulting in \(y = 2x + 10\).

Compare The Slopes Of The Two Equations

With both equations in slope-intercept form, it can be seen that the coefficient of \(x\) in each equation is equal, both being \(2\). Therefore, the slopes of both lines are equal.