Problem 28 - Algebra 1: Concepts and Skills

Question

Graph the equation. $$y=2 x-1$$

Step-by-Step Solution

Answer

The graph of \(y = 2x - 1\) is a straight line passing through the points (0, -1) and (1, 1).

Step 1: Identify the Slope and the Intercept

The equation provided is in slope-intercept form: \(y = 2x - 1\). Here, \(m = 2\) is the slope and \(c = -1\) is the y-intercept.

Step 2: Plot the Y-Intercept

The y-intercept is the point where the line crosses the y-axis. This happens when \(x = 0\). In this equation, the y-intercept is \(-1\). Therefore, plot a point at (0, -1) on the graph.

Step 3: Use the Slope to Find Another Point

The slope of the line is \(\frac{rise}{run}\) or \(\frac{change\ in\ y}{change\ in\ x}\). Here, the slope is \(2 = \frac{2}{1}\), which means for every 1 unit move to right along x-axis (run), we move 2 units upwards along the y-axis (rise). Start at the y-intercept (0, -1) and do this to find a second point. So, the second point is (1,1).

Step 4: Draw the Line

Use the points identified in steps 2 and 3 to draw a straight line that passes through these points. The line extending through (0,-1) and (1,1) represents the equation \(y = 2x - 1\).