# Khan/khan-exercises

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 Point slope form
randRangeNonZero( -5, 5 ) randRangeNonZero( -5, 5 ) randRangeNonZero( -5, 5 ) randRangeNonZero( -5, 5 ) (Y1 - Y2) / (X1 - X2)

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?

Y2 SLOPE X2
Y1 SLOPE X1

(y - \space) = \space(x - \space)

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})

randRangeNonZero( -5, 5 ) randRangeNonZero( -5, 5 ) randRangeNonZero( -5, 5 ) randRangeNonZero( -5, 5 ) (Y1 - Y2) / (X1 - 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.

Y2 SLOPE X2
Y1 SLOPE X1

(y - \space) = \space(x - \space)

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})

0 randRangeNonZero( -5, 5 ) randRangeNonZero( -5, 5 ) randRangeNonZero( -5, 5 ) (Y1 - Y2)/ (X1 - 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.

Y1 SLOPE X1

(y - \space) = \space(x - \space)

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})

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