A sand dune stands 5 feet above sea level. The hill is eroding at a rate of 1 foot per 20 years. Let y represent the height of the sand dune after x years. Which equation represents the situation?
y = negative StartFraction 1 Over 20 EndFraction x minus 5
y = negative StartFraction 1 Over 20 EndFraction x + 5
y = negative 20 x minus 5
y = negative 20 x + 5
y = negative StartFraction 1 Over 20 EndFraction x + 5
Kelsey graphed the equation y = 3x + 1 as shown below.
On a coordinate plane, a line goes through points (negative 3, 0) and (0, 3).
Which describes Kelsey’s error?
Kelsey graphed the y-intercept on the x-axis.
Kelsey graphed –3 instead of 3 as the y-intercept.
Kelsey graphed the slope as up 1 right 1 instead of up 1 left 1.
Kelsey graphed the slope as the y-intercept and the y-intercept as the slope.
Kelsey graphed -3 instead of 3 as the y-intercept.
The equation y = negative StartFraction 1 Over 20 EndFraction x + 10 represents the gallons of gasoline that remain in Michelle’s car after she drives x miles. Which graph represents this equation?
A graph titled Driving has total miles traveled on the x-axis and gallons of gasoline on the y-axis. A line goes through points (0, 10) and (40, 8).
A graph titled Driving has total miles traveled on the x-axis and gallons of gasoline on the y-axis. A line goes through points (0, 11) and (80, 8).
A graph titled Driving has total miles traveled on the x-axis and gallons of gasoline on the y-axis. A line goes through points (0, 12) and (125, 6).
A graph titled Driving has total miles traveled on the x-axis and gallons of gasoline on the y-axis. A line goes through points (0, 10) and (150, 0).
A graph titled Driving has total miles traveled on the x-axis and gallons of gasoline on the y-axis. A line goes through points (0, 10) and (40, 8).
Carey correctly graphs a linear function. The slope of the function is –1. The y-intercept is 3. Which is Carey’s graph?
On a coordinate plane, a line goes through points (0, 3) and (3, 0).
On a coordinate plane, a line goes through points (negative 3, 0) and (0, 3).
On a coordinate plane, a line goes through points (0, negative 1) and (1, 2).
On a coordinate plane, a line goes through points (negative 1, 2) and (0, negative 1).
The equation that represents the situation is y = -1/20x + 5.
To understand why, let's break down the given information and how it relates to the equation:
1. The sand dune stands 5 feet above sea level: This means that when x is 0 (initially), the height of the dune (y) is 5. Therefore, one part of the equation should be y = x + 5, to represent the initial height of the sand dune.
2. The hill is eroding at a rate of 1 foot per 20 years: This means that for every 20 years that pass, the sand dune decreases in height by 1 foot. To represent this rate of erosion, we need to subtract a fraction or fraction-based expression from the equation.
Since the erosion rate is -1 foot per 20 years (subtracting from the initial height of the dune), the fraction -1/20 represents this rate. Therefore, the equation becomes y = -1/20x + 5, where the term -1/20x represents the erosion and +5 represents the initial height.