Question

How do you write the equation of a line in slope intercept, point slope and standard form given (4,2) parallel to y=2x+3?

Answer 1

`(y-2)=2(x-4)` (in point slope forms) or `y=2x-6` (in slope intercept form) or `2x-y-6=0` (in standard form).

Explanation:

The equation of a line in slope intercept form is given as `y=mx+c`, where `m` is the slope of line and `c` is intercept formed by it on `y`-axis.

Point slope form is used to give equation of a line passing through a given point, say `(x_1,y_1)` and slope `m`. It is written as `(y-y_1)=m(x-x_1)`.

Standard form of equation is in the form `ax+by+c=0`.

In the given equation, `y=2x+3` is already in slope-intercept form and its slope is `2`. Slope of any line parallel to it will also be `2`.

To find the equation of a line passing through `(4,2)` with a slope of `2`, we use point slope form ad the equation is given by

`(y-2)=2(x-4)` or `y-2=2x-8` or `y=2x-6` (in slope intercept form) or `2x-y-6=0` (in standard form).