Question

graph the line. $y=2x-7$

Explanation:

Step1: Identify y-intercept

The equation $y=2x-7$ is in slope-intercept form $y=mx+b$, where $b=-7$. So the y-intercept is the point $(0, -7)$.

Step2: Identify slope

The slope $m=2$, which is $\frac{2}{1}$. This means for every 1 unit increase in $x$, $y$ increases by 2 units.

Step3: Find a second point

Starting from $(0, -7)$, move 1 unit right (increase $x$ by 1) and 2 units up (increase $y$ by 2). This gives the point $(0+1, -7+2)=(1, -5)$.

Step4: Plot and connect points

Plot the points $(0, -7)$ and $(1, -5)$, then draw a straight line through them extending across the grid.

Answer:

The line $y=2x-7$ is graphed by plotting the y-intercept $(0, -7)$, using the slope $\frac{2}{1}$ to find a second point $(1, -5)$, and drawing a straight line through these points.