Question

graph this line:
\\( y - 5 = -\frac{7}{6}(x - 3) \\)
click to select points on the graph.

Explanation:

Step1: Identify point from point-slope form

The equation $y - 5 = -\frac{7}{6}(x - 3)$ is in point-slope form $y-y_1=m(x-x_1)$, where $(x_1,y_1)=(3,5)$.

Step2: Find a second point using slope

Slope $m=-\frac{7}{6}$, meaning $\frac{\Delta y}{\Delta x}=-\frac{7}{6}$. From $(3,5)$, add 6 to $x$ and subtract 7 from $y$:
$x=3+6=9$, $y=5-7=-2$. So the second point is $(9,-2)$.

Step3: Verify with y-intercept (optional)

Rewrite equation to slope-intercept form:
$y = -\frac{7}{6}x + \frac{21}{6} + 5$
$y = -\frac{7}{6}x + \frac{7}{2} + 5$
$y = -\frac{7}{6}x + \frac{17}{2}$
When $x=0$, $y=\frac{17}{2}=8.5$, so the y-intercept is $(0, 8.5)$.

Answer:

Plot the points $(3, 5)$, $(9, -2)$, and $(0, 8.5)$, then draw a straight line connecting them to graph the line.