Question

find the lines slope and a point on the line.
y + 2 = \frac{1}{4}(x - 3)
slope:
point on the line: ( , )

Explanation:

Step1: Recall 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 of the line and \((x_1,y_1)\) is a point on the line.

Step2: Identify Slope and Point

Given the equation \(y + 2=\frac{1}{4}(x - 3)\), we can rewrite it in the point - slope form as \(y-(-2)=\frac{1}{4}(x - 3)\).
Comparing with \(y - y_1=m(x - x_1)\), we see that the slope \(m = \frac{1}{4}\) and the point \((x_1,y_1)=(3,- 2)\) (since \(x_1 = 3\) and \(y_1=-2\) as \(y-(-2)\) corresponds to \(y - y_1\) and \(x - 3\) corresponds to \(x - x_1\)).

Answer:

slope: \(\frac{1}{4}\)
point on the line: \((3,-2)\)