Question

a line has a slope of 7 and passes through the point (-1, -8). write its equation in slope-intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Recall the point - slope form

The point - slope form of a line is given by \(y - y_1=m(x - x_1)\), where \(m\) is the slope and \((x_1,y_1)\) is a point on the line. We know that \(m = 7\) and the point \((x_1,y_1)=(-1,-8)\).
Substitute these values into the point - slope form: \(y-(-8)=7(x - (-1))\), which simplifies to \(y + 8=7(x + 1)\).

Step2: Expand the right - hand side

Using the distributive property \(a(b + c)=ab+ac\), where \(a = 7\), \(b=x\) and \(c = 1\), we get \(y+8 = 7x+7\).

Step3: Solve for \(y\) (slope - intercept form \(y=mx + b\))

Subtract 8 from both sides of the equation: \(y=7x+7 - 8\).
Simplify the right - hand side: \(y=7x-1\).

Answer:

\(y = 7x-1\)