Question

practice c. write an equation for a line parallel to the given equation that contains the given point.

1. 3x + y = -5; (-3,7)
2. y = -x + 4; (-2,5)
3. 4x + 5y = 25; (5,-3)
4. y + 2 = (1/3)(x + 6); (6,0)

Explanation:

Problem 9:

Step1: Find slope of given line

Rewrite \(3x + y = -5\) as \(y = -3x - 5\). Slope \(m = -3\).

Step2: Use point - slope form

Point - slope: \(y - y_1 = m(x - x_1)\), \(x_1=-3,y_1 = 7,m=-3\)
\(y - 7=-3(x + 3)\)

Step3: Simplify

\(y - 7=-3x - 9\) → \(y=-3x - 2\) or \(3x + y=-2\)

Step1: Identify slope

Given \(y=-x + 4\), slope \(m=-1\).

Step2: Apply point - slope

Point \((-2,5)\), \(y - 5=-1(x + 2)\)

Step3: Simplify

\(y - 5=-x - 2\) → \(y=-x + 3\)

Step1: Find slope of given line

Rewrite \(4x + 5y = 25\) as \(y=-\frac{4}{5}x + 5\). Slope \(m =-\frac{4}{5}\).

Step2: Use point - slope

Point \((5,-3)\), \(y+3=-\frac{4}{5}(x - 5)\)

Step3: Simplify

\(y+3=-\frac{4}{5}x + 4\) → \(y=-\frac{4}{5}x + 1\) or \(4x+5y = 5\)

Answer:

\(3x + y=-2\) (or \(y=-3x - 2\))

Problem 10: