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})=\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}{X1}, \color{#b22222}{Y1}) and (\color{#4169E1}{X2}, \color{#4169E1}{Y2}). Express the equation of the line in point slope form.
(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}{fractionReduce(Y1 - Y2, X1 - X2)} and the y-intercept is \color{#4169E1}{Y1}. Express the equation of the line in point slope form.
(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})