Question

classify the pair of equations.
$-x + 3y = 18$
$y - 8 = \frac{1}{3}(x - 6)$
show your work here
○ the same line
○ perpendicular lines
○ distinct parallel lines
○ intersecting but not perpendicular lines

Explanation:

Step1: Rewrite first equation to slope-intercept form

Solve $-x + 3y = 18$ for $y$:
$3y = x + 18$
$y = \frac{1}{3}x + 6$

Step2: Rewrite second equation to slope-intercept form

Simplify $y - 8 = \frac{1}{3}(x - 6)$:
$y - 8 = \frac{1}{3}x - 2$
$y = \frac{1}{3}x + 6$

Step3: Compare slopes and intercepts

Both lines have slope $\frac{1}{3}$ and y-intercept $6$.

Answer:

The same line