Question

this question has two parts. first, answer part a. then, answer part b. part a solve the system by graphing. $y = -\frac{1}{2}x + 1$ $y = \frac{1}{2}x + 4$ graph both equations on the coordinate plane. tooling clues

Explanation:

Step1: Identify slope-intercept form

Both equations are in $y=mx+b$ form, where $m$=slope, $b$=y-intercept.
Equation 1: $y = -\frac{1}{2}x + 1$ (slope $m_1=-\frac{1}{2}$, y-intercept $b_1=1$)
Equation 2: $y = \frac{1}{2}x + 4$ (slope $m_2=\frac{1}{2}$, y-intercept $b_2=4$)

Step2: Graph first line

Plot y-intercept $(0,1)$. Use slope: move 2 right, 1 down to $(2,0)$. Draw line through points.

Step3: Graph second line

Plot y-intercept $(0,4)$. Use slope: move 2 right, 1 up to $(2,5)$. Draw line through points.

Step4: Find intersection point

Set equations equal: $-\frac{1}{2}x + 1 = \frac{1}{2}x + 4$
Solve for $x$:
$-\frac{1}{2}x - \frac{1}{2}x = 4 - 1$
$-x = 3$
$x = -3$
Substitute $x=-3$ into $y=\frac{1}{2}x + 4$:
$y = \frac{1}{2}(-3) + 4 = -\frac{3}{2} + 4 = \frac{5}{2}$
Intersection: $(-3, \frac{5}{2})$

Answer:

The solution to the system is $\boldsymbol{(-3, \frac{5}{2})}$ (or $(-3, 2.5)$). When graphed, the two lines intersect at this point.