Solutions

1. \(-5\) (Written Solution)

   We are trying to find the slope of the line that connects the points \((10, -9)\) and \((7, 6)\).

   Remember, \({\text{Slope}}={\text{m}}=\frac{\text{rise}}{\text{run}}=\frac{{\text{y}}_{2}-{\text{y}}_{1}}{{\text{x}}_{2}-{\text{x}}_{1}}\)

   Step 1: Decide which ordered pair is point 1, and which is point 2. For this problem \({\color{Red} (10,-9)}\) will be point 1 and \((7, 6)\) will be point 2.

   (Note: It doesn’t matter which is which, just as long as you are consistent throughout the problem.)

   Step 2: Substitute the values of the two points into the formula and simplify:

   \(\frac{{\color{Blue}{\text{y}}_{2}}-{\color{Red}{\text{y}}_{1}}}{{\color{Blue}{\text{x}}_{2}}-{\color{Red}{\text{x}}_{1}}} = \frac{{\color{Blue}6}-{\color{Red}(-9)}}{{\color{Blue}7}-{\color{Red}10}} = \frac{15}{-3} = -5\)

   So the slope of the line is \(-5\).



2. \(-2\)


3. \(-6\)


4. \(\frac{3}{2}\) (Written Solution)

   We are trying to find the slope of the line that connects the coordinate points \((3, 5)\) and \((13, 20)\). Remember, \({\text{Slope}}={\text{m}}=\frac{\text{rise}}{\text{run}}=\frac{{\text{y}}_{2}-{\text{y}}_{1}}{{\text{x}}_{2}-{\text{x}}_{1}}\)

   Step 1: Decide which ordered pair is point 1, and which is point 2. For this problem (3, 5) will be point 1 and (13, 20) will be point 2.

   (Note: It doesn’t matter which is which, just as long as you are consistent throughout the problem.)

   Step 2: Substitute the values of the two points into the formula and simplify:

   \(\frac{\text{rise}}{\text{run}}=\frac{{\color{Blue}{\text{y}}_{2}}-{\color{Red}{\text{y}}_{1}}}{{\color{Blue}{\text{x}}_{2}}-{\color{Red}{\text{x}}_{1}}} = \frac{{\color{Blue}20}-{\color{Red}5}}{{\color{Blue}13}-{\color{Red}3}} = \frac{15}{10}\)

   We can divide the numerator and denominator by 5 since it is a common factor of both, so \(\frac{15}{10}\) simplifies to \(\frac{3}{2}\)

   So the slope of the line is \(\frac{3}{2}\)



5. \(\frac{1}{3}\)


6. \(\frac{3}{5}\)