(a) Write the equation in slope-intercept form, and determine the slope and $y$-intercept.
(b) Graph the equation using the slope and $y$-intercept.
[tex]$-2 y+1=-7$[/tex]
Answer (1)
Rewrite the given equation in slope-intercept form: y = 4 .
Identify the slope: m = 0 .
Identify the y-intercept: b = 4 .
Graph the horizontal line y = 4 passing through the point ( 0 , 4 ) .
y = 4 , m = 0 , b = 4
Explanation
Understanding the Problem We are given the equation − 2 y + 1 = − 7 and asked to (a) write it in slope-intercept form and determine the slope and y -intercept, and (b) graph the equation using the slope and y -intercept.
Solving for y To write the equation in slope-intercept form, we need to solve for y . The slope-intercept form is y = m x + b , where m is the slope and b is the y -intercept.
Isolating the y term First, subtract 1 from both sides of the equation: − 2 y + 1 − 1 = − 7 − 1
− 2 y = − 8
Solving for y Next, divide both sides by -2: − 2 − 2 y = − 2 − 8
y = 4
Identifying Slope and y-intercept (a) The equation in slope-intercept form is y = 0 x + 4 or simply y = 4 . The slope m is 0, and the y -intercept b is 4.
Graphing the Equation (b) To graph the equation, we plot the y -intercept at ( 0 , 4 ) . Since the slope is 0, the line is horizontal.
Examples
Understanding slope and y-intercept is crucial in many real-world applications. For example, imagine you are tracking the altitude of an airplane during a level flight. If the altitude remains constant at 4000 feet, the equation representing this situation is y = 4000 , where y is the altitude. The slope is 0, indicating no change in altitude, and the y-intercept is 4000, representing the initial and constant altitude. This concept helps in understanding and predicting various constant relationships in science, engineering, and economics.
