Question

question
what is the equation of the line that passes through the point (-2, 0) and has a slope of 2?

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.
Here, \(x_1=-2\), \(y_1 = 0\) and \(m = 2\).
Substitute these values into the point - slope form: \(y-0=2(x - (-2))\)

Step2: Simplify the equation

Simplify the right - hand side of the equation:
\(y=2(x + 2)\)
Expand the right - hand side using the distributive property \(a(b + c)=ab+ac\), where \(a = 2\), \(b=x\) and \(c = 2\).
\(y=2x+4\)

Answer:

The equation of the line is \(y = 2x+4\) (or in standard form \(2x-y=- 4\))