Graph the line y=2x - 3
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Step-by-Step Solution
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 12. 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.