Using the following values, create an equation in point slope form. In other words, given the values below, for a formula that looks like `(y - y_{1}) = m(x - x_{1})`

, what are the values of `x_{1}`

, `y_{1}`

, and `m`

?

`x_{1}=\color{#b22222}{`

`X1`},\quad f(x_{1})=\color{#b22222}{`Y1`}.`x_{2}=\color{#4169E1}{`

`X2`},\quad f(x_{2})\text{ } = \color{#4169E1}{`Y2`}.

`(y - {}`

`) = {}`

`(x - {}`

`)`

integers, like `6`

*simplified proper* fractions, like `3/5`

*simplified improper* fractions, like `7/4`

and/or *exact* decimals, like `0.75`

pay attention to the sign of each number you enter to be sure the entire equation is correct

`f(x)`

is just a fancy term for `y`

. So one point is `(\color{#b22222}{`

.`X1`}, \color{#b22222}{`Y1`})

The formula to find the slope is: `m = (y_{1} - y_{2}) / (x_{1} - x_{2})`

.

So, by plugging in the numbers, we get `\displaystyle {} \frac{\color{#b22222}{`

`Y1`} - (\color{#4169E1}{`Y2`})}{\color{#b22222}{`X1`} - (\color{#4169E1}{`X2`})} =`\color{#68228B}{\dfrac{`

`Y1-Y2`}{` X1-X2`}} =`\color{#68228B}{`

`fractionReduce(Y1 - Y2, X1 - X2)`}

Select one of the points to substitute for `x_{1}`

and `y_{1}`

in the point slope formula. The solution is then either:

`(y - \color{#b22222}{`

`Y1`}) = \color{#68228B}{`fractionReduce(Y1 - Y2, X1 - X2)`}(x - \color{#b22222}{`X1`})

OR

`(y - \color{#4169E1}{`

`Y2`}) = \color{#68228B}{`fractionReduce(Y1 - Y2, X1 - X2)`}(x - \color{#4169E1}{`X2`})

A line passes through both `(\color{#b22222}{`

and `X1`}, \color{#b22222}{`Y1`})`(\color{#4169E1}{`

. Express the equation of the line in point slope form.`X2`}, \color{#4169E1}{`Y2`})

`(y - {}`

`) = {}`

`(x - {}`

`)`

integers, like `6`

*simplified proper* fractions, like `3/5`

*simplified improper* fractions, like `7/4`

and/or *exact* decimals, like `0.75`

pay attention to the sign of each number you enter to be sure the entire equation is correct

The formula to find the slope is: `m = (y_{1} - y_{2}) / (x_{1} - x_{2})`

.

So, by plugging in the numbers, we get `\displaystyle {} \frac{\color{#b22222}{`

`Y1`} - (\color{#4169E1}{`Y2`})}{\color{#b22222}{`X1`} - (\color{#4169E1}{`X2`})} =`\color{#68228B}{\dfrac{`

`Y1-Y2`}{` X1-X2`}} =` \color{#68228B}{`

`fractionReduce(Y1 - Y2, X1 - X2)`}

Select one of the points to substitute for `x_{1}`

and `y_{1}`

in the point slope formula. The solution then becomes either:

`(y - \color{#b22222}{`

`Y1`}) = \color{#68228B}{`fractionReduce(Y1 - Y2, X1 - X2)`}(x - \color{#b22222}{`X1`})

OR

`(y - \color{#4169E1}{`

`Y2`}) = \color{#68228B}{`fractionReduce(Y1 - Y2, X1 - X2)`}(x - \color{#4169E1}{`X2`})

The slope of a line is `\color{#68228B}{`

and the y-intercept is `fractionReduce(Y1 - Y2, X1 - X2)`}`\color{#4169E1}{`

. Express the equation of the line in point slope form.`Y1`}

`(y - {}`

`) = {}`

`(x - {}`

`)`

integers, like `6`

*simplified proper* fractions, like `3/5`

*simplified improper* fractions, like `7/4`

and/or *exact* decimals, like `0.75`

pay attention to the sign of each number you enter to be sure the entire equation is correct

The y-intercept is the value of `y`

when `x = 0`

, so it defines a point you can use:`\quad(\color{#b22222}{`

.`X1`}, \color{#b22222}{`Y1`})

An equation in point slope form looks like: `(y - y_{1}) = m(x - x_{1})`

Thus, the solution in point slope form can be written as:`(y - \color{#b22222}{`

`Y1`}) = \color{#68228B}{`fractionReduce(Y1 - Y2, X1 - X2)`}(x - \color{#b22222}{`X1`})