The graph should look like a line with a slope of
passing through the point (0, 4).
To graph the equation
, we can start by rewriting it in slope-intercept form
, where
is the slope and
is the y-intercept.
![\[y - 3 = (1)/(2)(x + 2)\]](https://img.qammunity.org/2022/formulas/mathematics/high-school/g73xtv9adq10ops72jcldngn4dqxitpac7.png)
Distribute the
on the right side:
![\[y - 3 = (1)/(2)x + 1\]](https://img.qammunity.org/2022/formulas/mathematics/high-school/8kw0xgfokhs00kqe6eanf8efe3ukjx2ta8.png)
Now, add 3 to both sides to isolate \(y\):
![\[y = (1)/(2)x + 4\]](https://img.qammunity.org/2022/formulas/mathematics/high-school/i0a2i1yd4if00p6g6ei2v230ee9fi3umuq.png)
Now, you can see that the slope
is
, and the y-intercept
is 4.
To graph this equation, plot the y-intercept at (0, 4) and use the slope to find additional points. For example, if you move one unit to the right (increase x by 2), you would move up
units. Connect these points to draw the line.
Therefore the graph should look like a line with a slope of
passing through the point (0, 4).