Question

integrated math 1 | m7a hw1 name: chaistcine michel period: 1
solve the systems of equations by graphing.

1. $y=\frac{2}{3}x-2$ m=__ b=__

$y=2x+2$ m=__ b=__
solution: (__,__)

1. $y=-\frac{3}{2}x+5$ m=__ b=__

$y=-\frac{2}{3}x+5$ m=__ b=__
solution: (__,__)

1. $y=-\frac{1}{2}x+2$ m=__ b=__

$y=-3x-3$ m=__ b=__

1. $y=-3$ m=__ b=__

$y=x-3$ m=__ b=__

Explanation:

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Problem 1

Step1: Identify slope/intercept

For $y=\frac{2}{3}x-2$: $m=\frac{2}{3}$, $b=-2$
For $y=2x+2$: $m=2$, $b=2$

Step2: Solve algebraically (check)

Set equations equal:
$\frac{2}{3}x - 2 = 2x + 2$
Multiply by 3: $2x - 6 = 6x + 6$
Rearrange: $-4x = 12$ → $x=-3$
Substitute $x=-3$: $y=2(-3)+2=-4$

Answer:

$(-3, -4)$

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Problem 2

Step1: Identify slope/intercept

For both $y=-\frac{3}{2}x+5$: $m=-\frac{3}{2}$, $b=5$

Step2: Analyze system

Same line → infinitely many solutions