Question

find a point on the line and the lines slope.
$y + 2 = 3(x + 3)$
point on the line: (□,□)
slope: □

Explanation:

Step1: Recall point - slope form

The point - slope form of a line is given by \(y - y_1=m(x - x_1)\), where \((x_1,y_1)\) is a point on the line and \(m\) is the slope of the line. We can rewrite the given equation \(y + 2=3(x + 3)\) in the form \(y-(-2)=3(x - (-3))\).

Step2: Identify the point and slope

By comparing \(y-(-2)=3(x - (-3))\) with the point - slope form \(y - y_1=m(x - x_1)\), we can see that \(x_1=- 3\), \(y_1=-2\) and \(m = 3\). So a point on the line is \((-3,-2)\) and the slope of the line is \(3\).

Answer:

point on the line: \((-3,-2)\)
slope: \(3\)