Question

line v has an equation of 7x + y = -5. line w includes the point (-1, 7) and is parallel to line v. what is the equation of line w? write the equation in slope - intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Explanation:

Step1: Find slope of line v

Rewrite \(7x + y = -5\) in slope - intercept form \(y=mx + b\) (where \(m\) is slope).
Subtract \(7x\) from both sides: \(y=-7x - 5\). So slope of line v, \(m=-7\).

Step2: Determine slope of line w

Parallel lines have equal slopes. So slope of line w, \(m=-7\).

Step3: Use point - slope form to find equation of line w

Point - slope form is \(y - y_1=m(x - x_1)\), where \((x_1,y_1)=(-1,7)\) and \(m = - 7\).
Substitute values: \(y - 7=-7(x - (-1))\)
Simplify the right - hand side: \(y - 7=-7(x + 1)\)

Step4: Convert to slope - intercept form

Expand the right - hand side: \(y - 7=-7x-7\)
Add 7 to both sides: \(y=-7x-7 + 7\)
Simplify: \(y=-7x\)

Answer:

\(y = - 7x\)