Question

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4th six weeks, week 2 homework
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1. (2,4) slope = \\(\frac{1}{2}\\)

equation:

1. (2, -3) slope = 3

equation:

1. (-4, -3) and (8,0)

equation:

1. (1,9) and (-2, -6)

equation:
write an equation that is either parallel or perpendicular

Explanation:

Step1: Use point-slope formula (Q14)

Given $(x_1,y_1)=(2,4)$, $m=\frac{1}{2}$. Substitute into $y-y_1=m(x-x_1)$:
$y-4=\frac{1}{2}(x-2)$
Simplify to slope-intercept form:
$y=\frac{1}{2}x - 1 + 4$
$y=\frac{1}{2}x + 3$

Step2: Use point-slope formula (Q15)

Given $(x_1,y_1)=(2,-3)$, $m=3$. Substitute into $y-y_1=m(x-x_1)$:
$y-(-3)=3(x-2)$
Simplify to slope-intercept form:
$y+3=3x - 6$
$y=3x - 9$

Step3: Calculate slope first (Q16)

Given $(x_1,y_1)=(-4,-3)$, $(x_2,y_2)=(8,0)$. Slope formula:
$m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-(-3)}{8-(-4)}=\frac{3}{12}=\frac{1}{4}$
Substitute into point-slope formula:
$y-(-3)=\frac{1}{4}(x-(-4))$
Simplify:
$y+3=\frac{1}{4}x + 1$
$y=\frac{1}{4}x - 2$

Step4: Calculate slope first (Q17)

Given $(x_1,y_1)=(1,9)$, $(x_2,y_2)=(-2,-6)$. Slope formula:
$m=\frac{y_2-y_1}{x_2-x_1}=\frac{-6-9}{-2-1}=\frac{-15}{-3}=5$
Substitute into point-slope formula:
$y-9=5(x-1)$
Simplify:
$y-9=5x - 5$
$y=5x + 4$

Answer:

1. $y=\frac{1}{2}x + 3$
2. $y=3x - 9$
3. $y=\frac{1}{4}x - 2$
4. $y=5x + 4$