Question

What is the equation of the line passing through `(13,-4)` and `(14,-9)`?

Answer 1

`y + 4 = -5(x-13)`

Explanation:

I'm not sure which form of equation you want it to be in, but going to show the simplest, or point-slope form, which is `y - y_1 = m(x-x_1)`.

First, we need to find the slope of the line, `m`.

To find the slope, we use the formula `m = (y_2-y_1)/(x_2-x_1)`, also known as "rise over run", or change of `y` over change of `x`.

Our two coordinates are `(13, -4)` and `(14, -9)`. So let's plug those values into the slope equation and solve:
`m = (-9-(-4))/(14-13)`
`m = -5/1`
`m = -5`

Now, we need a set of coordinates from the given or the graph. Let's use the point `(13, -4)`

So our equation is:
`y-(-4) = -5(x-13)`

Simplified...
`y + 4 = -5(x-13)`

Answer 2

`y=-5x+61`

Explanation:

`"the equation of a line in "color(blue)"slope-intercept form"` is.

`•color(white)(x)y=mx+b`

`"where m is the slope and b the y-intercept"`

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

`color(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_1-y_1)/(x_2-x_1))color(white)(2/2)|)))`

`"let "(x_1,y_1)=(13,-4)" and "(x_2,y_2)=(14-9)`

`rArrm=(-9-(-4))/(14-13)=-5`

`rArry=-5x+blarrcolor(blue)"is the partial equation"`

`"to find b use either of the two given points"`

`"using "(13,-4)`

`-4=-65+brArrb=61`

`rArry=-5x+61larrcolor(red)"in slope-intercept form"`