Question

Are the graphs of y=3x-5 and 9x+3y=1 parallel, perpendicular or neither?

Answer 1

Answer:

The two lines are neither parallel nor perpendicular to one another.

Step-by-step explanation:

The slope $m$ gives the orientation of a line.

Make sure that the equation of both lines are in the slope-intercept form $y = m\, x + b$ (where $m\!$ is the slope and $b$ is the $y$-intercept) before comparing their slopes.

The equation of the first line $y = 3\, x - 5$ is already in the slope-intercept form. Compare this equation with the standard $y = m\, x + b$. The slope of this line would be $m = 3$.

Rewrite the equation of the second line $9\, x + 3\, y = 1$ to obtain the slope-intercept equation of that line:

$3\, y = -9\, x + 1$.

$\displaystyle y = -3\, x + \frac{1}{3}$.

Thus, the slope of this line would be $m = (-3)$.

Two lines are parallel to one another if and only if their slopes are equal. In this question, $3 \ne (-3)$. Thus, the two lines are not parallel to one another.

On the other hand, two lines are perpendicular to one another if and only if the product of their slopes is $(-1)$. In this question, $3\times (-3) = (-9)$, which is not $(-1)\!$. Thus, these two lines are not perpendicular to one another, either.