Question

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

m: b:
equation:

6.

m: b:
equation:

7.

x	-2	-16	-28	-40

m: b:
equation:

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

m: b:
equation:

9.

m: b:
equation:

10.

x	25	15	-5	-20

m: b:
equation:

Explanation:

Problem 5: (-14,-15) and (-57,-58)

Step1: Calculate slope $m$

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

Step2: Find y-intercept $b$

Use $y = mx + b$, substitute $x=-14, y=-15, m=1$:
$-15 = 1\times(-14) + b \implies b = -15 +14 = -1$

Step3: Write linear equation

$y = mx + b$

Step1: Identify two points on line

Points: $(-3,1)$ and $(2,3)$

Step2: Calculate slope $m$

$m = \frac{3 - 1}{2 - (-3)} = \frac{2}{5} = 0.4$

Step3: Find y-intercept $b$

Substitute $x=-3, y=1, m=\frac{2}{5}$ into $y=mx+b$:
$1 = \frac{2}{5}\times(-3) + b \implies b = 1 + \frac{6}{5} = \frac{11}{5} = 2.2$

Step4: Write linear equation

$y = mx + b$

Step1: Calculate slope $m$

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

Step2: Find y-intercept $b$

Substitute $x=-2, y=-3, m=-\frac{5}{2}$ into $y=mx+b$:
$-3 = -\frac{5}{2}\times(-2) + b \implies -3 = 5 + b \implies b = -8$

Step3: Verify with another point

Check $x=-28, y=62$: $62 = -\frac{5}{2}\times(-28) -8 = 70 -8 = 62$ (valid)

Step4: Write linear equation

$y = mx + b$

Answer:

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

---

Problem 6: Graph of line