In order to determine the relationship between the lines, let's calculate each of their slopes.

Slope of $R S$

We are given the points

R (1, 1)

and

S (9, 8),

which lie on

R S .

Let's substitute them into the Slope Formula and calculate the slope.

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

SubstitutePoints

Substitute $(1, 1)$ & $(9, 8)$

m_{1} = \frac{8 - 1}{9 - 1}

SubTerms

Subtract terms

m_{1} = \frac{7}{8}

Slope of $J K$

Similarly, by substituting the points

J (- 6, 1)

and

K (2, 8)

into the Slope Formula, we can calculate the slope of

J K .

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

SubstitutePoints

Substitute $(- 6, 1)$ & $(2, 8)$

m_{2} = \frac{8 - 1}{2 - ( - 6 )}

SubNeg

$a - (- b) = a + b$

m_{2} = \frac{8 - 1}{2 + 6}

AddSubTerms

Add and subtract terms

m_{2} = \frac{7}{8}

Analyze the Slopes

Now that we know the slopes of the lines, we can determine whether they are parallel, perpendicular, or neither. Remember that parallel slopes are the same and perpendicular slopes are opposite reciprocals.

m_{1} = \frac{7}{8} m_{2} = \frac{7}{8}

These slopes are the same, so the lines are parallel.

Graph

Let's graph the lines to verify that they are parallel. We do can this by plotting the points and drawing lines through them.

As we can see, the lines are truly parallel.

Slope of RS

Slope of JK

Analyze the Slopes

Graph

Slope of $R S$

Slope of $J K$

Exercise 54 Page 343

Hints

Check the answer

Practice exercises

Asses your skill

Slope of RS

Slope of JK

Analyze the Slopes

Graph

Slope of $R S$

Slope of $J K$