Question

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

Explanation:

Step1: Identify slope and y-intercept

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

Step2: Plot the y-intercept

The y-intercept is the point where the line crosses the y-axis. This is the point $(0, 1)$.

Step3: Use slope to find a second point

Slope $\frac{2}{3}$ means $\frac{\text{rise}}{\text{run}}=\frac{2}{3}$. From $(0,1)$, move up 2 units and right 3 units to get the point $(3, 3)$.

Step4: Draw the line

Connect the points $(0,1)$ and $(3,3)$ with a straight line, extending it in both directions.

Answer:

The line passes through points $(0, 1)$ and $(3, 3)$, with a slope of $\frac{2}{3}$, extending infinitely in both directions.