Question

the slope of a roof is \\(\frac{1}{4}\\). if a coordinate plane is overlaid on an image of this roof, the roof starts from the bottom left at \\((0, 0)\\). which equation best represents the appearance of the left side of the roof?\
\\(\circ\\) \\(y = \frac{1}{4}x\\)\
\\(\circ\\) \\(4x + y = 1\\)\
\\(\circ\\) \\(y = 4x\\)\
\\(\circ\\) \\(y - 1 = \frac{1}{4}(x - 1)\\)

Explanation:

Step1: Identify known values

We know the slope $m=\frac{1}{4}$, and the line passes through $(0,0)$.

Step2: Use slope-intercept form

The slope-intercept formula is $y=mx+b$, where $b$ is the y-intercept. Since the line passes through $(0,0)$, $b=0$.

Step3: Substitute values into formula

Substitute $m=\frac{1}{4}$ and $b=0$ into $y=mx+b$:
$y=\frac{1}{4}x + 0$
Simplify to get $y=\frac{1}{4}x$.

Step4: Verify with graph

The left side of the roof goes from $(0,0)$ to the peak at $x=2$. Plugging $x=2$ into $y=\frac{1}{4}x$ gives $y=\frac{1}{4}(2)=\frac{1}{2}$, which matches the upward slope of the left roof segment on the graph.

Answer:

$\boldsymbol{y=\frac{1}{4}x}$