Kevin plotted a linear equation on a graph with 18 as the y-intercept. Which of the following could be the equation plotted by Kevin?
To determine which of the given options could be the equation plotted by Kevin, we need to understand the equation of a line and how it relates to its graph.
The equation of a line in slope-intercept form is given by:
y = mx + b
where:
- y is the dependent variable (vertical axis on the graph)
- x is the independent variable (horizontal axis on the graph)
- m is the slope of the line
- b is the y-intercept, which is the value of y when x = 0 (the point where the line intersects the y-axis)
In this case, we are given that the y-intercept is 18. This means that when x = 0, y = 18.
Let's analyze each of the given options:
a) y = 2x
b) y = -3x + 18
c) y = 4x + 18
d) y = 18x + 9
To verify if an equation is correct, we can substitute x = 0 into the equation and check if it gives us the correct y-intercept, which is 18.
a) y = 2(0) = 0
- The equation y = 2x does not yield a y-intercept of 18.
b) y = -3(0) + 18 = 18
- The equation y = -3x + 18 yields a y-intercept of 18.
c) y = 4(0) + 18 = 18
- The equation y = 4x + 18 also yields a y-intercept of 18.
d) y = 18(0) + 9 = 9
- The equation y = 18x + 9 does not yield a y-intercept of 18.
Based on our analysis, options b) and c) could be the equations plotted by Kevin, as they both yield a y-intercept of 18.
Therefore, the correct answer is either b) y = -3x + 18 or c) y = 4x + 18.