Question

unit 4 lesson 3: homework
point of intersection
graph the equations.
find the point of intersection.
1.
$y = -\frac{5}{3}x + 3$
$y = \frac{1}{3}x - 3$
poi
(-3, 8)
graph
2.
$y = 4x + 3$
$y = -x - 2$
poi
( , )
graph
3.
$y = -\frac{1}{2}x - 1$
$y = \frac{1}{4}x - 4$
poi
( , )
graph
4.
$y = -1$
$y = -\frac{5}{2}x + 4$
poi
( , )
graph

Explanation:

Problem 2:

Step1: Set equations equal

Since \( y = 4x + 3 \) and \( y = -x - 2 \), set \( 4x + 3 = -x - 2 \).

Step2: Solve for \( x \)

Add \( x \) to both sides: \( 5x + 3 = -2 \).
Subtract 3: \( 5x = -5 \).
Divide by 5: \( x = -1 \).

Step3: Find \( y \)

Substitute \( x = -1 \) into \( y = -x - 2 \): \( y = -(-1) - 2 = 1 - 2 = -1 \).

Step1: Set equations equal

Set \( -\frac{1}{2}x - 1 = \frac{1}{4}x - 4 \).

Step2: Solve for \( x \)

Multiply all terms by 4: \( -2x - 4 = x - 16 \).
Add \( 2x \): \( -4 = 3x - 16 \).
Add 16: \( 12 = 3x \).
Divide by 3: \( x = 4 \).

Step3: Find \( y \)

Substitute \( x = 4 \) into \( y = \frac{1}{4}x - 4 \): \( y = \frac{1}{4}(4) - 4 = 1 - 4 = -3 \).

Step1: Substitute \( y = -1 \)

Substitute \( y = -1 \) into \( y = -\frac{5}{2}x + 4 \): \( -1 = -\frac{5}{2}x + 4 \).

Step2: Solve for \( x \)

Subtract 4: \( -5 = -\frac{5}{2}x \).
Multiply by \( -\frac{2}{5} \): \( x = 2 \).

Answer:

\((-1, -1)\)

Problem 3: