Question

A line passes through point (3, 7) and has a slope of `3/4`. What is the equation of this line?

Answer 1

Point slope form: `y-7=3/4(x-3)`

Slope intercept form: `y=3/4x+19/4` `color(white)(..)"or"color(white)(..)` `y=3/4x+4 3/4`

Explanation:

Since you have one point and the slope, you can use the point slope formula, then solve for `y` to get the slope intercept form, so that you can determine the y-intercept `(b)`. Then you can graph the resulting equation.

Point slope formula
`y-y_1=m(x-x_1)`, where `x_1,y_1=(3,7)`, and `m=3/4` is the slope.

Substitute the given values into the formula.

`y-7=3/4(x-3)`

Expand.

`y-7=3/4x-9/4`

Solve for `y` to get the slope intercept form: `y=mx+b`, where `m=3/4` is the slope and `b` is the y-intercept.

`y-7=3/4x-9/4`

Add `7` to both sides.

`y-color(red)cancel(color(black)(7))+color(red)cancel(color(black)(7))=3/4x-9/4+7`

Simplify.

`y=3/4x-9/4+7`

In order to add and subtract fractions, they must have the same denominator. `7=7/1` and can be multiplied by the equivalent fraction `color(red)(4/4)` in order to get the same denominator as `9/4`.

`y=3/4x-9/4+7/1xxcolor(red)(4/4)`

Simplify.

`y=3/4x-9/4+28/4`

Simplify.

`y=3/4x+19/4` or

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

The y-intercept is `19/4`

graph{y=3/4x+19/4 [-17.42, 14.6, -5.96, 10.06]}

Answer 2

`"answer :"`

`y=3/4x-37/4`

`"Or "`

`-3x+4y=-37`

Explanation:

`"equation for solution is "`

`y-y_1=m(x-x_1)`

`"where " P(x_1,y_1)=P(3,7)`

`y-7=3/4(x-3)`

`y=3/4(x-3)+7`

`y=3/4x-9/4+7`

`y=3/4x-37/4`

`"Or "`

`y-3/4x=-37/4`

`(4y-3x)/4=-37/4`

`(4y-3x)/cancel(4)=-37/cancel(4)`

`-3x+4y=-37`