Question

systems by graphing e/m solve each system by graphing. 1). $y = \frac{1}{2}x + 4$ $y = -\frac{3}{2}x - 2$

Explanation:

Step1: Identify slope-intercept form

Both equations are in $y=mx+b$ form, where $m$=slope, $b$=y-intercept.

1. $y=\frac{1}{2}x + 4$: $m=\frac{1}{2}$, $b=4$
2. $y=-\frac{5}{2}x - 2$: $m=-\frac{5}{2}$, $b=-2$

Step2: Find intersection algebraically

Set equations equal to solve for $x$:
$$\frac{1}{2}x + 4 = -\frac{5}{2}x - 2$$
Multiply all terms by 2 to eliminate denominators:
$$x + 8 = -5x - 4$$

Step3: Solve for $x$

Rearrange to isolate $x$ terms:
$$x + 5x = -4 - 8$$
$$6x = -12$$
$$x = \frac{-12}{6} = -2$$

Step4: Solve for $y$

Substitute $x=-2$ into $y=\frac{1}{2}x + 4$:
$$y = \frac{1}{2}(-2) + 4 = -1 + 4 = 3$$

Answer:

The solution (intersection point) is $(-2, 3)$

To graph:

1. For $y=\frac{1}{2}x + 4$: plot y-intercept $(0,4)$, then use slope $\frac{1}{2}$ (up 1, right 2) to plot a second point.
2. For $y=-\frac{5}{2}x - 2$: plot y-intercept $(0,-2)$, then use slope $-\frac{5}{2}$ (down 5, right 2) to plot a second point.
3. Draw lines through each set of points; they intersect at $(-2, 3)$