Question

example 3 (page 110)
find the slope of each line.
7.
8.
9.
example 4 (page 311)
find the slope of the line that passes through each pair of points.

1. (3, 2), (5, 6)
2. (5, 6), (3, 2)
3. (4, 8), (8, 11)
4. (-4, 4), (2, -5)
5. (-2, 1), (1, -2)
6. (-3, 1), (3, -5)
7. (-8, 0), (1, 5)
8. (0, 0), (3, 5)
9. (-4, -5), (-9, 1)
10. (5, 0), (0, 2)
11. (-7, 1), (7, 8)
12. (0, -1), (1, -6)

example 5 (page 311)
state whether the slope is zero or undefined.
22.
23.

1. (3, 4), (-3, 4)
2. (4, 3), (4, -3)
3. (left(-5, \frac{1}{2}

ight), (-5, 3))
skills
find the rate of change for each situation.

1. a baby is 18 in. long at birth and 27 in. long at ten months.
2. the cost of group museum tickets is $48 for four people and $78 for ten people.
3. you drive 30 mi in one hour and 120 mi in four hours.

find the slope of the line passing through each pair of points.

1. (-7, 1), (7, 8)
2. (left(4, 1\frac{2}{3}

ight), left(-2, \frac{2}{3}
ight))

1. (0, 3.5), (-4, 2.5)
2. (left(\frac{1}{2}, 8

ight), (1, -2))

1. (left(-5, \frac{1}{2}

ight), (-5, 3))

1. (0.5, 6.25), (3, -1.25)

through the given point, draw the line with the given slope.

1. (k(3, 5))

slope (-2)

1. (m(5, 2))

slope (-\frac{1}{2})

1. (q(-2, 3))

slope (\frac{3}{5})

1. (r(2, -3))

slope (-\frac{4}{3})

1. a. biology which line in the graph at the left is the steepest?

b. during the 6 - week period, which plant had the greatest rate of change? the least rate of change? how do you know?

1. a. find the slope of the line through (a(4, -3)) and (b(1, -5)) using (a) for ((x_2, y_2)) and (b) for ((x_1, y_1)).

b. find the slope of the line in part (a) using (b) for ((x_2, y_2)) and (a) for ((x_1, y_1)).
c. critical thinking explain why it does not matter which point you use for ((x_2, y_2)) and which point you use for ((x_1, y_1)) when you calculate a slope.

Explanation:

Let's solve problem 10: Find the slope of the line that passes through the points \((3, 2)\) and \((5, 6)\).

Step 1: Recall the slope formula

The slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\).

Step 2: Identify the coordinates

For the points \((3, 2)\) and \((5, 6)\), we have \(x_1 = 3\), \(y_1 = 2\), \(x_2 = 5\), and \(y_2 = 6\).

Step 3: Substitute into the slope formula

Substitute the values into the formula: \(m=\frac{6 - 2}{5 - 3}\).

Step 4: Simplify the expression

First, calculate the numerator: \(6 - 2 = 4\). Then, calculate the denominator: \(5 - 3 = 2\). So, \(m=\frac{4}{2}=2\).

Answer:

The slope of the line passing through \((3, 2)\) and \((5, 6)\) is \(2\).