Question

What is the slope of the line that passes through (3 ,5) and (-3,-5) ?

Answer 1

`"slope "=5/3`

Explanation:

`"to calculate the slope m use the "color(blue)"gradient formula"`

`•color(white)(x)m=(y_2-y_1)/(x_2-x_1)`

`"let "(x_1,y_1)=(3,5)" and "(x_2,y_2)=(-3,-5)`

`rArrm=(-5-5)/(-3-3)=(-10)/(-6)=10/6=5/3`

Answer 2

`y=5/3x+c`, where the slope is `5/3` and the `y` intercept is `+2`

Explanation:

The slope of a line can be found out using:

Change in `y` // change in `x`

Where the first coordinate is `x`, and the second coordinates are `y`

`therefore` `3 -> -6` you have to `-6`

`therefore` `5 -> -5` you have to `-10`

`therefore` `-> (-10)/-6 -> 5/3` when dividing by `3`.

Remember a negative divided by a negative gets a positive.

If wanting to find the full equation, we have to find the `y` intercept as this is in the form:

`y=mx+c` where `m` is the gradient `(5/3)` and `c` is the `y` intercept.

So far we have:

`y=5/3x+c`

We can substitute in the `y` value, and the slope.

Using the coordinates `(3,5)`

`5=5/3 xx 3+c`

`5=3+c`

`therefore` `c=2`

using `y=mx+c`

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