Question

1. $y - 1 = \frac{4}{5}(x + 5)$

Explanation:

Assuming the problem is to convert the given equation to slope - intercept form (\(y=mx + b\)) or find the slope and a point on the line. Let's assume we want to convert it to slope - intercept form.

Step1: Distribute the fraction

We have the equation \(y - 1=\frac{4}{5}(x + 5)\). Using the distributive property \(a(b + c)=ab+ac\), where \(a = \frac{4}{5}\), \(b=x\) and \(c = 5\), we get \(y-1=\frac{4}{5}x+\frac{4}{5}\times5\)
\(y-1=\frac{4}{5}x + 4\)

Step2: Solve for y

Add 1 to both sides of the equation.
\(y=\frac{4}{5}x+4 + 1\)
\(y=\frac{4}{5}x+5\)

Answer:

In slope - intercept form, the equation is \(y=\frac{4}{5}x + 5\) (if the goal was to convert to slope - intercept form). If the goal was to identify the slope and a point: the slope \(m=\frac{4}{5}\) and a point on the line is \((- 5,1)\) (since the point - slope form is \(y - y_1=m(x - x_1)\) and our equation is \(y - 1=\frac{4}{5}(x-(-5))\))