Question

graph the line with the equation $y = \frac{2}{3}x + 1$.

Explanation:

Step1: Identify the slope and y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the equation \(y=\frac{2}{3}x + 1\), the slope \(m=\frac{2}{3}\) 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 y - axis.

Step3: Use the slope to find another point

The slope \(m=\frac{2}{3}\) means "rise over run", or \(\frac{\text{change in }y}{\text{change in }x}\). From the point \((0,1)\), we rise 2 units (since the numerator of the slope is 2) and run 3 units to the right (since the denominator of the slope is 3). This gives us the point \((0 + 3,1+2)=(3,3)\).

Step4: Draw the line

Draw a straight line through the points \((0,1)\) and \((3,3)\) (and extend it in both directions).

Answer:

To graph \(y=\frac{2}{3}x + 1\), plot \((0,1)\) (y - intercept), then use the slope \(\frac{2}{3}\) to find \((3,3)\) and draw a line through these points.