Question

What is the equation of the line which is parallel to the line 3x +4y =6 and passes through (2, 1)?

Show work and explain please.

Answer 1

`y=-3/4x+5/2`

Explanation:

.
`3x+4y=6`

Let's solve for `y` so we can have the equation in standard slope-intercept form:

`4y=-3x+6`

`y=-3/4x+3/2`

This is in the form of:

`y=mx+b` where `m` is slope and `b` is the `y`-intercept which is where the line crosses the `y`-axis. Comparing the two we see that:

`m=-3/4` and `b=3/2`

For a line to be parallel to this line, it would have to have the same slope, i.e. its equation would be:

`y=-3/4x+b`

Now, we can use the coordinates of the point the line goes through and plug them into this equation to solve for `b`:

`1=-3/4(2)+b`

`1=-3/2+b`

`b=1+3/2=2/2+3/2=5/2`

Therefore, the equation of the line is:

`y=-3/4x+5/2`