Question

question
what is the equation of the line that passes through the point (2, -3) 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, $x_1 = 2$, $y_1=-3$ and $m = 2$.

Step2: Substitute values into point - slope form

Substitute $x_1 = 2$, $y_1=-3$ and $m = 2$ into the point - slope formula:
$y-(-3)=2(x - 2)$
Simplify the left - hand side: $y + 3=2(x - 2)$

Step3: Expand and simplify to slope - intercept form (optional, but to get the general form)

Expand the right - hand side: $y+3 = 2x-4$
Subtract 3 from both sides: $y=2x-4 - 3$
So, $y=2x-7$ (in slope - intercept form $y=mx + b$) or in standard form $2x-y=7$ (by rearranging $y=2x - 7$ to $2x-y-7 = 0$ or $2x - y=7$)

Answer:

The equation of the line is $y = 2x-7$ (or $2x - y=7$)