Question

graph the line that has a slope of $-\frac{1}{5}$ and includes the point (5, 6).
click to select points on the graph.

Explanation:

Step1: Use point-slope form

The point-slope formula is $y - y_1 = m(x - x_1)$, where $m=-\frac{1}{5}$, $x_1=5$, $y_1=6$.
$y - 6 = -\frac{1}{5}(x - 5)$

Step2: Simplify to slope-intercept form

Expand and isolate $y$.
$y - 6 = -\frac{1}{5}x + 1$
$y = -\frac{1}{5}x + 7$

Step3: Find a second point

Use slope $\frac{\Delta y}{\Delta x}=-\frac{1}{5}$. From $(5,6)$, add 5 to $x$, subtract 1 from $y$: $(5+5, 6-1)=(10,5)$.

Answer:

Plot the points $(5, 6)$ and $(10, 5)$, then draw a straight line through them. The line can also be extended to include other points like $(0, 7)$.