Example 11.17 from Prealgebra, 11.2 Graphing Linear Equations

Graphing Linear Equations: example 11.17

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

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Find three points that are solutions to the equation. Since this equation has the fraction $\frac{1}{2}$ as a coefficient of $x,$ we will choose values of $x$ carefully. We will use zero as one choice and multiples of $2$ for the other choices.

The points are shown in the table.

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

$x$ $y$ $(x, y)$

$0$ $3$ $(0, 3)$

$2$ $4$ $(2, 4)$

$4$ $5$ $(4, 5)$

Plot the points, check that they line up, and draw the line as shown.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Graph the equation: $y = \frac{1}{3} x - 1 .$

How did it go?