Writing Linear Functions

In this exercise, we will examine Ron-Jon's incorrect solution when he tried to find the slope of a line. Let's begin by writing the slope formula.

slope = \frac{rise}{run} \Leftrightarrow m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}

In the formula,

m

represents the slope, and

(x_{1}, y_{1})

and

(x_{2}, y_{2})

represent points that lie on the line. Let's find the slope by ourselves and compare our results to determine the mistake Ron-Jon made. To do so, we will substitute

(5, 4)

and

(- 1, 16)

for

(x_{1}, y_{1})

and

(x_{2}, y_{2}),

respectively.

m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}

SubstitutePointsSubstitute

(5, 4)

&

(- 1, 16)

m = \frac{1 6 - 4}{- 1 - 5}

Right away we can see Ron-Jon's error. The points were wrongly substituted into the formula. Basically, he calculated run over rise rather than rise over run. Let's continue and find the correct slope.

m = \frac{1 6 - 4}{- 1 - 5}

SubTermsSubtract terms

m = \frac{1 2}{- 6}

MoveNegNumToFracPut minus sign in front of fraction

m = - \frac{1 2}{6}

CalcQuotCalculate quotient

m = - 2

The correct slope is

- 2 .

Writing Linear Functions 1.8 - Solution