Question

3
for use after lessons 3.3 - 3.4
find the value of x that makes m || n.
1.
2.
3.
find the slope of the line that passes through the given points.

1. (2, - 2); (6, 6)
2. (3, 4), (5, 6)
3. (-4, 3), (-9, 7)

Explanation:

1.

Step1: Use the property of alternate interior angles

When \(m\parallel n\), \(4x = 84\) (alternate interior angles are equal).

Step2: Solve for \(x\)

Divide both sides of the equation \(4x=84\) by \(4\), \(x=\frac{84}{4}=21\).

2.

Step1: Use the property of same - side exterior and interior angles

When \(m\parallel n\), \((2x + 5)+135=180\) (same - side exterior and interior angles are supplementary).

Step2: Simplify the equation

\(2x+140 = 180\).

Step3: Solve for \(x\)

Subtract \(140\) from both sides: \(2x=180 - 140=40\). Then divide by \(2\), \(x = 20\).

3.

Step1: Use the property of corresponding angles

When \(m\parallel n\), \(3x-8=70\) (corresponding angles are equal).

Step2: Solve for \(x\)

Add \(8\) to both sides: \(3x=70 + 8=78\). Then divide by \(3\), \(x = 26\).

4.

Step1: Use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\)

Let \((x_1,y_1)=(2,-2)\) and \((x_2,y_2)=(6,6)\). Then \(m=\frac{6-(-2)}{6 - 2}\).

Step2: Simplify the formula

\(m=\frac{6 + 2}{4}=\frac{8}{4}=2\).

5.

Step1: Use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\)

Let \((x_1,y_1)=(3,4)\) and \((x_2,y_2)=(5,6)\). Then \(m=\frac{6-4}{5 - 3}\).

Step2: Simplify the formula

\(m=\frac{2}{2}=1\).

6.

Step1: Use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\)

Let \((x_1,y_1)=(-4,3)\) and \((x_2,y_2)=(-9,7)\). Then \(m=\frac{7 - 3}{-9-(-4)}\).

Step2: Simplify the formula

\(m=\frac{4}{-9 + 4}=\frac{4}{-5}=-\frac{4}{5}\).

Answer:

1. \(21\)
2. \(20\)
3. \(26\)
4. \(2\)
5. \(1\)
6. \(-\frac{4}{5}\)