Question

1. (-14,-15) and (-57,-58)

x y
m: b:
equation:

6.

m: b:
equation:

7.
x -2 -16 -28 -40
y -3 32 62 92
m: b:
equation:

1. (-40,77) and (-15,32)

x y
m: b:
equation:

9.

m: b:
equation:

10.
x y
25 17
15 23
-5 35
-20 44
m: b:
equation:

Explanation:

Problem 5:

Step1: Calculate slope m

Formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{-58-(-15)}{-57-(-14)}=\frac{-43}{-43}=1$

Step2: Find y-intercept b

Use point $(-14,-15)$: $y=mx+b$
$-15=1\times(-14)+b$ → $b=-15+14=-1$

Step3: Write equation

$y=mx+b$
$y=x-1$

Problem 7:

Step1: Calculate slope m

Use points $(-2,-3)$ and $(-16,32)$
$m=\frac{32-(-3)}{-16-(-2)}=\frac{35}{-14}=-2.5=-\frac{5}{2}$

Step2: Find y-intercept b

Use point $(-2,-3)$: $y=mx+b$
$-3=-\frac{5}{2}\times(-2)+b$ → $-3=5+b$ → $b=-8$

Step3: Write equation

$y=-\frac{5}{2}x-8$

Problem 8:

Step1: Calculate slope m

Formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{32-77}{-15-(-40)}=\frac{-45}{25}=-1.8=-\frac{9}{5}$

Step2: Find y-intercept b

Use point $(-40,77)$: $y=mx+b$
$77=-\frac{9}{5}\times(-40)+b$ → $77=72+b$ → $b=5$

Step3: Write equation

$y=-\frac{9}{5}x+5$

Problem 9:

Step1: Identify points from graph

Use $(0,-4)$ and $(2,0)$

Step2: Calculate slope m

$m=\frac{0-(-4)}{2-0}=\frac{4}{2}=2$

Step3: Find y-intercept b

From y-intercept point $(0,-4)$, $b=-4$

Step4: Write equation

$y=2x-4$

Problem 10:

Step1: Calculate slope m

Use points $(25,17)$ and $(15,23)$
$m=\frac{23-17}{15-25}=\frac{6}{-10}=-0.6=-\frac{3}{5}$

Step2: Find y-intercept b

Use point $(25,17)$: $y=mx+b$
$17=-\frac{3}{5}\times25+b$ → $17=-15+b$ → $b=32$

Step3: Write equation

$y=-\frac{3}{5}x+32$

Answer:

Problem 5:

m: $1$, b: $-1$, Equation: $y=x-1$

Problem 7:

m: $-\frac{5}{2}$, b: $-8$, Equation: $y=-\frac{5}{2}x-8$

Problem 8:

m: $-\frac{9}{5}$, b: $5$, Equation: $y=-\frac{9}{5}x+5$

Problem 9:

m: $2$, b: $-4$, Equation: $y=2x-4$

Problem 10:

m: $-\frac{3}{5}$, b: $32$, Equation: $y=-\frac{3}{5}x+32$