Question

What is the equation of the line with slope `m= 7/25` that passes through `(47/5 32/10)`?

Answer 1

`y=7/25x+71/125`

Explanation:

Given:

`P_1(x_1;y_1)`

The equation of a line through a point is:

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

`:.y-32/10=7/25*(x-47/5)`

`y=7/25x-329/125+color(green)cancel(32)^color(green)16/color(green)cancel(10)^color(green)5`

`y=7/25x+(-329+400)/125`

`y=7/25x+71/125`

Answer 2

The equation in slope-intercept form is `y=7/25x+71/125`.

Explanation:

We can use the slope-intercept form of a straight line, `y=mx+b`, where slope, `m` is `7/25`, `x=47/5`, and `y=32/10`.

Notice that we don't know the y-intercept, `b`. Rearrange the equation to isolate `b`, substitute the given values and solve.

`y=mx+b`

`b=y-mx`

`b=32/10-(7/25)(47/5)`

Simplify.

`b=32/10-(329)/(125)`

Simplify `32/10` to `16/5`.

`b=16/5-329/125`

The LCD is `125`. Multiply `16/5` times `25/25`.

`b=16/5(25/25)-329/125`

Simplify.

`b=400/125-329/125`

Simplify.

`b=71/125`

The equation in slope-intercept form is `y=7/25x+71/125`.