What's the slope of the line that contains the points (4,8) and (9,8)? What type of line is it?
A) The line has no slope; it's a vertical line.
B) Slope = 0; horizontal line
C) The line has no slope; it's a horizontal line.
D) Slope = 0; vertical line
Answer (1)
Calculate the slope using the formula m = x 2 − x 1 y 2 − y 1 .
Substitute the given points (4,8) and (9,8) into the formula: m = 9 − 4 8 − 8 .
Simplify the expression to find the slope: m = 0 .
Conclude that the line is horizontal because the slope is 0, so the final answer is Slope = 0; horizontal line .
Explanation
Problem Analysis We are given two points (4,8) and (9,8) and asked to find the slope of the line that contains them and determine the type of line.
Slope Formula To find the slope of the line, we use the formula: m = x 2 − x 1 y 2 − y 1 , where ( x 1 , y 1 ) = ( 4 , 8 ) and ( x 2 , y 2 ) = ( 9 , 8 ) .
Calculating the Slope Plugging in the coordinates, we get: m = 9 − 4 8 − 8 = 5 0 = 0
Determining the Type of Line Since the slope is 0, the line is a horizontal line. A horizontal line has a slope of 0, meaning that the y-value remains constant for all x-values.
Final Answer Therefore, the slope of the line is 0, and it is a horizontal line. The correct answer is B) Slope = 0; horizontal line
Examples
Imagine you're tracking the altitude of an airplane during a short period. If the altitude remains constant, the graph of altitude versus time would be a horizontal line. The slope of this line is 0, indicating no change in altitude. This concept is useful in various real-world scenarios, such as understanding constant rates, flat surfaces, or stable conditions.
