Graph the line $y = 2x - 3$

Step 1: Identify the equation type

The given equation $y = 2x - 3$ is in the slope-intercept form, $y = mx + c$. In this form, $m$ represents the slope of the line and $c$ represents the $y$ -intercept.

Step 2: Determine slope and y-intercept

By comparing $y = 2x - 3$ with $y = mx + c$, we can identify the slope $m = 2$ and the $y$ -intercept $c = -3$. The $y$ -intercept is the point where the line crosses the $y$ -axis, which is $(0, -3)$.

Step 3: Plot the y-intercept

First, we plot the $y$ -intercept. Since $c = -3$, the line crosses the $y$ -axis at the point $(0, -3)$.

Step 4: Use the slope to find another point

The slope $m = 2$ can be written as $\frac{2}{1}$. This means for every 1 unit we move to the right (run), we move 2 units up (rise). Starting from the $y$ -intercept $(0, -3)$, we move 1 unit right and 2 units up to find a second point, which is $(0+1, -3+2) = (1, -1)$.

Step 5: Draw the line

With two points, $(0, -3)$ and $(1, -1)$, we can now draw a straight line that passes through both of them. This line represents the graph of the equation $y = 2x - 3$.

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