Question

1. points: (4, -5) and (-8, -14)

equation: ______________

1. points: (-5, -3) and (-15, -7)

equation: ______________

Explanation:

Step1: Find the slope (m)

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).

For Problem 9 (Points: (4, -5) and (-8, -14)):

\(x_1 = 4\), \(y_1=-5\), \(x_2=-8\), \(y_2 = -14\)
\(m=\frac{-14-(-5)}{-8 - 4}=\frac{-14 + 5}{-12}=\frac{-9}{-12}=\frac{3}{4}\)

For Problem 10 (Points: (-5, -3) and (-15, -7)):

\(x_1=-5\), \(y_1 = -3\), \(x_2=-15\), \(y_2=-7\)
\(m=\frac{-7-(-3)}{-15-(-5)}=\frac{-7 + 3}{-15 + 5}=\frac{-4}{-10}=\frac{2}{5}\)

Step2: Use point - slope form \(y - y_1=m(x - x_1)\) to find the equation

For Problem 9:

Using point \((4,-5)\) and \(m = \frac{3}{4}\)
\(y-(-5)=\frac{3}{4}(x - 4)\)
\(y + 5=\frac{3}{4}x-3\)
\(y=\frac{3}{4}x-3 - 5\)
\(y=\frac{3}{4}x-8\)
Multiply through by 4 to get standard form (if needed): \(4y=3x - 32\) or \(3x-4y = 32\)

For Problem 10:

Using point \((-5,-3)\) and \(m=\frac{2}{5}\)
\(y-(-3)=\frac{2}{5}(x-(-5))\)
\(y + 3=\frac{2}{5}(x + 5)\)
\(y+3=\frac{2}{5}x + 2\)
\(y=\frac{2}{5}x+2 - 3\)
\(y=\frac{2}{5}x-1\)
Multiply through by 5 to get standard form (if needed): \(5y=2x - 5\) or \(2x-5y = 5\)

Answer:

Problem 9 Equation: \(y=\frac{3}{4}x - 8\) (or \(3x - 4y=32\))

Problem 10 Equation: \(y=\frac{2}{5}x-1\) (or \(2x - 5y = 5\))