Question

graph this line using the slope and y-intercept:
$y = -\frac{7}{6}x + 2$
click to select points on the graph.

Explanation:

Step1: Identify y-intercept

The equation is in slope-intercept form $y=mx+b$, where $b$ is the y-intercept. Here, $b=2$, so the y-intercept point is $(0, 2)$.

Step2: Identify the slope

From $y = -\frac{7}{6}x + 2$, the slope $m=-\frac{7}{6}$, meaning $\frac{\text{change in } y}{\text{change in } x}=-\frac{7}{6}$.

Step3: Find a second point

Starting from $(0,2)$, move 6 units right (change in $x=+6$) and 7 units down (change in $y=-7$). This gives the point $(0+6, 2-7)=(6, -5)$.

Step4: Draw the line

Plot the points $(0,2)$ and $(6,-5)$, then draw a straight line through them.

Answer:

The line passes through points $(0, 2)$ and $(6, -5)$, with a slope of $-\frac{7}{6}$ and y-intercept at $(0,2)$.