Graph y-3=1/2(x-2)

$y - 3 = \frac{1}{2} (x - 2)$

Step 1

Move all terms not containing $y$ to the right side of the equation.

Add $3$ to both sides of the equation.

$y = \frac{x}{2} - 1 + 3$

Add $- 1$ and $3$ .

$y = \frac{x}{2} + 2$

Step 2

Rewrite in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Reorder terms.

$y = \frac{1}{2} x + 2$

Step 3

Use the slope-intercept form to find the slope and y-intercept.

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = \frac{1}{2}$

$b = 2$

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $\frac{1}{2}$

y-intercept: $(0, 2)$

Slope: $\frac{1}{2}$

y-intercept: $(0, 2)$

Step 4

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

Reorder terms.

$y = \frac{1}{2} x + 2$

Create a table of the $x$ and $y$ values.

$\begin{array}{c} x & y \\ 0 & 2 \\ 2 & 3 \end{array}$

Step 5

Graph the line using the slope and the y-intercept, or the points.

Slope: $\frac{1}{2}$

y-intercept: $(0, 2)$

$\begin{array}{c} x & y \\ 0 & 2 \\ 2 & 3 \end{array}$

Step 6