Two different lines are shown below with two points given from each line. Use the slope-intercept form or point-slope form to find the equation of each line.

Question

Line A

Points: (–5, –2), (–5, 7)

Line B

Points: (7, –5), (–2, –5)

Line A has
.
The equation of line A is
.
Line B has
.
The equation of line B is
.

Answer 1

To find the equations of the lines given the points, we first determine the slopes and the types of each line.

Line A

Points: (–5, –2), (–5, 7)

Observation: Since both points have the same x-coordinate (-5), Line A is a vertical line.

• A vertical line has an undefined slope and is represented by the equation \( x = a \), where \( a \) is the x-coordinate of the line.

Equation of Line A: \[ x = -5 \]

Line B

Points: (7, –5), (–2, –5)

Observation: Since both points have the same y-coordinate (-5), Line B is a horizontal line.

• A horizontal line has a slope of 0 and is represented by the equation \( y = b \), where \( b \) is the y-coordinate of the line.

Equation of Line B: \[ y = -5 \]

Summary

• Line A has a vertical slope.
• The equation of Line A is \( x = -5 \).
• Line B has a horizontal slope.
• The equation of Line B is \( y = -5 \).