Question

1. $y = -x + 7$ $y = x + 1$

Explanation:

Step1: Find intersection of two lines

To find the intersection of \( y = -x + 7 \) and \( y = x + 1 \), set them equal:
\( -x + 7 = x + 1 \)

Step2: Solve for x

Add \( x \) to both sides: \( 7 = 2x + 1 \)
Subtract 1: \( 6 = 2x \)
Divide by 2: \( x = 3 \)

Step3: Find y

Substitute \( x = 3 \) into \( y = x + 1 \): \( y = 3 + 1 = 4 \)
So intersection is \( (3, 4) \). Now, to graph:

• For \( y = -x + 7 \): when \( x = 0 \), \( y = 7 \); when \( y = 0 \), \( x = 7 \). Plot \( (0,7) \) and \( (7,0) \), draw line.
• For \( y = x + 1 \): when \( x = 0 \), \( y = 1 \); when \( y = 0 \), \( x = -1 \). Plot \( (0,1) \) and \( (-1,0) \), draw line. The lines intersect at \( (3,4) \).

Answer:

The intersection point of \( y = -x + 7 \) and \( y = x + 1 \) is \( (3, 4) \). To graph, plot the intercepts for each line and draw them, showing their intersection at \( (3, 4) \).