Slope From Graphs and Points
In the phrase rise/run, what does rise represent and what does run represent?
Rise is the vertical change. Run is the horizontal change.
In y = mx + b, what do m and b represent?
m is the slope. b is the y-intercept.
What two pieces of information do you need to write an equation in y = mx + b form?
The slope and the y-intercept.
What makes a relationship a function?
Each input has exactly one output.
Which quadrant contains the point (-3, 4)?
Quadrant II.
Find the slope between (1, 2) and (5, 10).
m = (10 - 2)/(5 - 1) = 8/4 = 2.
For y = 3x - 4, identify the slope and y-intercept.
Slope = 3; y-intercept = -4.
Write the equation of a line with slope -4 and y-intercept 7.
y = -4x + 7.
Is {(-1, 2), (0, 5), (-1, 7), (2, 9)} a function? Explain.
No. The input -1 has two different outputs, 2 and 7.
Translate the point (2, -5) left 3 units and up 7 units.
(-1, 2).
Find the slope of the line through (-2, 4) and (3, -6).
m = (-6 - 4)/(3 - (-2)) = -10/5 = -2.
For y = -2x + 5, what point do you plot first, and what slope movement do you use next?
Start at (0, 5), then go down 2 and right 1.
Write the equation for the table: x = 0, 1, 2, 3 and y = 5, 8, 11, 14.
y = 3x + 5.
If a vertical line crosses a graph twice, is the graph a function? Why?
No. One input would have two outputs.
Reflect the point (6, -2) over the y-axis.
(-6, -2).
A wheelchair ramp rises 3 feet over a horizontal run of 12 feet. What is the slope of the ramp?
3/12 = 1/4.
A line has y-intercept -1 and slope 3/2. Write its equation and name two points on the line.
y = (3/2)x - 1. Examples: (0, -1) and (2, 2).
A gym charges a $30 starting fee plus $12 each month. Write an equation for total cost y after x months.
y = 12x + 30.
A table has y-values 3, 7, 11, and 15 when x increases by 1 each time. Is it linear or nonlinear? Explain.
Linear. The y-values increase by a constant amount of 4.
A right triangle has legs 9 and 12. What is the length of the hypotenuse?
15.
A line passes through A(-4, -1) and B(2, 8). Find the slope and tell whether the line rises or falls from left to right.
m = (8 - (-1))/(2 - (-4)) = 9/6 = 3/2. The line rises.
Which graph is steeper: y = 2x + 1 or y = 5x - 4? Explain using slope.
y = 5x - 4 is steeper because the absolute value of its slope is greater: 5 > 2.
A taxi costs $6 after 1 mile and $18 after 5 miles. Write a linear equation for cost y after x miles.
Slope = 3 and y-intercept = 3, so y = 3x + 3.
A savings pattern goes 5, 10, 20, 40 as the week number increases by 1. Is it linear or nonlinear? Explain.
Nonlinear. The values are multiplying by 2, not increasing by a constant amount.
Find the distance between (1, -2) and (7, 6).
10.