Question

How do you find a standard form equation for the line with slope 2/3 that passes through the point (3,6)?

Answer 1

You may use the standard form of the straight line:

`y=mx+b`, where `m` is the slope and `b` the y-intercept

Explanation:

The statement gives that `m=2/3`, so we have to find the value of `b`

Now, we also know that the line passes through `(3, 6)`, and so:

`6 = 2/3*3+ b` and then `6=2 + b` and so `b=4`. The equation of the line is then:

`y=2/3 x + 4`

Answer 2

The standard form is `2x - 3y = - 12`

Explanation:

Start by finding the slope-intercept form of the equation, then converting that to the standard form.

The slope-intercept form is
`y = mx + b`

The slope `m` is given as `2/3`, so the equation up to that point is
`y = (2)/(3)x + b`

To find `b`, sub in the values for `x` and `y` from the ordered pair given in the problem.

`6 = (2)/(3)((3)/(1)) + b`
Solve for `b`

1) Clear the parentheses by multiplying the fractions
`6 = 2 + b`

2) Subtract `2` from both sides to isolate `b`
`4 = b`

So the slope-intercept form of the equation is
`y = (2/3)x + 4` `larr` slope-intercept form

Change the slope-intercept form into standard form.

Standard form is
`ax + by = c` where `a` is a positive whole digit

1) Clear the fraction by multiplying all the terms on both sides by `3` and letting the denominator cancel
`3y = 2x + 12`

2) Subtract `2x` from both sides to get the `x` and `y` terms on the same side
`- 2x + 3y = 12`

3) Multiply through by `-1` to clear the minus sign
`2x - 3y = - 12` `larr` standard form