Question

question
what is the equation of the line that passes through the point (1,2) 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, \(x_1 = 1\), \(y_1=2\) and \(m = 2\).

Step2: Substitute values into point - slope form

Substitute \(x_1 = 1\), \(y_1 = 2\) and \(m=2\) into the formula \(y - y_1=m(x - x_1)\):
\(y-2 = 2(x - 1)\)

Step3: Simplify the equation

Expand the right - hand side: \(y-2=2x-2\)
Add 2 to both sides of the equation: \(y=2x-2 + 2\), which simplifies to \(y = 2x\) (or in standard form \(2x-y=0\))

Answer:

The equation of the line is \(y = 2x\) (or \(2x - y=0\))