Question

graph the line with the equation $y = 2x - 1$.

Explanation:

Step1: Identify the slope and y - intercept

The equation of the line is in the slope - intercept form \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the equation \(y = 2x-1\), the slope \(m = 2=\frac{2}{1}\) and the y - intercept \(b=- 1\).

Step2: Plot the y - intercept

The y - intercept is \(b = - 1\), so we plot the point \((0,-1)\) on the coordinate plane.

Step3: Use the slope to find another point

The slope \(m=\frac{2}{1}\) means that from the point \((0,-1)\), we move up 2 units (because the numerator of the slope is 2) and then move 1 unit to the right (because the denominator of the slope is 1). So from \((0,-1)\), moving up 2 and right 1 gives us the point \((0 + 1,-1+2)=(1,1)\). We can also move down 2 units and left 1 unit from \((0,-1)\) to get another point \((0 - 1,-1-2)=(-1,-3)\).

Step4: Draw the line

Draw a straight line passing through the points we have plotted (e.g., \((0,-1)\), \((1,1)\), \((-1,-3)\)) to graph the line \(y = 2x-1\).

Answer:

To graph \(y = 2x - 1\):

1. Plot the y - intercept \((0,-1)\).
2. Use the slope \(m = 2\) to find additional points (e.g., from \((0,-1)\), move up 2, right 1 to get \((1,1)\) or down 2, left 1 to get \((-1,-3)\)).
3. Draw a straight line through the plotted points.