Question

the equation of line g is x - y = -7. line h, which is parallel to line g, includes the point (1, -7). what is the equation of line h? 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 g

Rewrite \(x - y=-7\) in slope - intercept form \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept).
Subtract \(x\) from both sides: \(-y=-x - 7\).
Multiply both sides by \(- 1\): \(y=x + 7\). So the slope of line \(g\), \(m = 1\).

Step2: Determine slope of line h

Since line \(h\) is parallel to line \(g\), parallel lines have the same slope. So the slope of line \(h\), \(m_h=1\).

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

The point - slope form of a line is \(y - y_1=m(x - x_1)\), where \((x_1,y_1)=(1,-7)\) and \(m = 1\).
Substitute the values: \(y-(-7)=1\times(x - 1)\).
Simplify: \(y + 7=x - 1\).

Step4: Rewrite in slope - intercept form

Subtract 7 from both sides: \(y=x-1 - 7\).
Simplify: \(y=x - 8\).

Answer:

\(y = x-8\)