graph the line.\ny = 2x + 3

Explanation:

Step1: Find the y - intercept

The equation is in slope - intercept form $y = mx + b$, where $b$ is the y - intercept. For $y = 2x+3$, when $x = 0$, $y=3$. So the y - intercept is the point $(0,3)$.

Step2: Find another point using the slope

The slope $m = 2=\frac{\Delta y}{\Delta x}$. Starting from the y - intercept $(0,3)$, if we increase $x$ by 1 ($\Delta x = 1$), then $\Delta y=2$. So when $x = 1$, $y=2\times1 + 3=5$, giving the point $(1,5)$.

Step3: Plot the points and draw the line

Plot the points $(0,3)$ and $(1,5)$ on the coordinate plane and draw a straight line passing through them.

Answer:

Plot the points $(0,3)$ and $(1,5)$ and draw a straight - line through them to graph $y = 2x+3$.