Question

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

Explanation:

Step1: Identify slope and y-intercept

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

Step2: Plot y-intercept point

The y-intercept is at $(0, 3)$; mark this point on the coordinate plane.

Step3: Use slope to find next point

Slope $\frac{1}{2}$ means $\frac{\text{rise}}{\text{run}} = \frac{1}{2}$. From $(0,3)$, move up 1 unit and right 2 units to get $(2, 4)$; mark this point.

Step4: Draw the straight line

Connect the points $(0, 3)$ and $(2, 4)$ with a straight line, extending it in both directions.

Answer:

The graph is a straight line passing through points $(0, 3)$ and $(2, 4)$, with a slope of $\frac{1}{2}$ and y-intercept at $(0, 3)$.