Unit 3: Slope, Rate of Change & Linear Equations · NY-8.F.3, NY-8.F.4, AI-F.LE.2
Both exams
Notes
Slope-intercept form. y = mx + b. m is the slope; b is the y-intercept, the value of y when x = 0. In a context, b is often a starting amount and m is the ongoing rate.
From two points to an equation. Find m, then substitute one point into y = mx + b to solve for b. Check with the second point.
Vocabulary
y-intercept: The point where a graph crosses the y-axis; the value of y when x = 0.
Practice (no calculator unless marked)
Which equation represents the graph of a line on a coordinate plane that passes through the x-intercept at (9, 0) and the y-intercept at (0, −5)?
A. y = −(9/5)x − 5
B. y = (9/5)x − 5
C. y = −(5/9)x − 5
D. y = (5/9)x − 5
Cory drinks water from a bottle during a bike ride. The average amount of water, in ounces, in his water bottle can be represented by the equation y = −8x + 32, where y is the amount of water remaining after x hours. Based on the equation, what amount of water, in ounces, will remain in the bottle after Cory rides for 2 1/2 hours?
A. 8
B. 12
C. 20
D. 32
Which linear equation represents a line that passes through the point (−3, −8)?
A. y = 2x − 2
B. y = 2x − 8
C. y = 2x + 13
D. y = 2x − 14
Function A: A taxi driver charges a base of $3.00 plus $2.00 per mile. Function B: y = 3x + 2, where x is miles and y is the total charge. Which statement correctly compares the functions?
A. Function A has both a greater rate of change and a greater initial value.
B. Function B has both a greater rate of change and a greater initial value.
C. Function A has a greater rate of change than Function B, but the initial value for Function A is less than the initial value for Function B.
D. Function B has a greater rate of change than Function A, but the initial value for Function B is less than the initial value for Function A.
The equation that represents the sequence −2, −5, −8, −11, −14, … is
A. aₙ = −3 + (−2)(n − 1)
B. aₙ = −2 + (−3)(n − 1)
C. aₙ = 3 + (−2)(n − 1)
D. aₙ = −2 + 3(n − 1)
Which equation represents the graph of a line on a coordinate plane that passes through the x-intercept at (9, 0) and the y-intercept at (0, −5)?
A. y = −(9/5)x − 5
B. y = (9/5)x − 5
C. y = −(5/9)x − 5
D. y = (5/9)x − 5
Cory drinks water from a bottle during a bike ride. The average amount of water, in ounces, in his water bottle can be represented by the equation y = −8x + 32, where y is the amount of water remaining after x hours. Based on the equation, what amount of water, in ounces, will remain in the bottle after Cory rides for 2 1/2 hours?
A. 8
B. 12
C. 20
D. 32
Which linear equation represents a line that passes through the point (−3, −8)?