Finding Slope of a Line
What form does the equation need to be in before we graph a linear function?
slope-intercept form y = mx + b
What is slope-intercept form?
y = mx + b
The first three terms of an arithmetic sequence are
10, 7, and 4. What is the common difference for this sequence?
-3
The snow is accumulating 1/2 inch every hour. The snow is already 3 inches high. Write an equation for the total amount of snow accumulated, y, as a function of the number of hours, x, that it has been snowing
y = 1/2x + 3
Identify the slope of the following equation. y = 2x + 3
slope is 2
When graphing linear equations, what point should we plot first?
the y-intercept
In the following linear equation, what is the y-intercept?
y = -3/4x
0
Which of the following equations represents a horizontal line that passes through the point (3, 9)?
(1) y = 3x + 9
(2) x = 3
(3) y = 9
(3) y = 9
George was picking bananas to give to his grandmother. His grandmother already has 5 bananas. George picks about 3 bananas every minute. Write an equation to represent the total number of bananas that George's grandmother will have, y, as a function of the number of minutes, x, George has been picking bananas.
y = 3x + 5
Name three ways to describe slope.
Possible answers:
rate of change
rise over run
(y2 - y1) / (x2 - x1)
change in y divided by change in x
slope = m in y = mx + b
Graph the following equation.
y = 1/3x + 4
Graph should start with the point at (0, 4). Movement should be up 1 and right 3.
Graph the following equation. 8x + 4y = 16
Should be rewritten as y = -2x + 4 and then graphed.
y-intercept = 4
Slope = -2 (down 2, right 1)
A large tub of water starts to drain when it is filled up with 100 gallons of water. It drains at a constant rate of 4 gallons per minute. If G represents the volume of water in the tub in gallons and t represents the time in minutes the tub has been draining, then which equation relates G and t?
(1) G = 100t - 4
(2) G = -4t + 100
(3) G = 4t +100
(2) G = -4t + 100
Find the slope of the line that includes the following points.
(4, -5) and (-4, 5)
-10/8 which simplifies to -5/4
Graph the following equation.
x = -2
VERTICAL line at x = -2
Rewrite the following equation in slope-intercept form.
3x + 6y = -18
y = -1/2x - 3
Graph the following function:
y = -|x - 2| + 7
Use your calculator and write down x and y values in a table.
Rebecca is a private tutor who is willing to travel to meet her clients. She charges an hourly rate and an additional charge for preparation and gas. She uses the function C(h) = 6h + 5 to determine how much to charge for tutoring. What does the constant term of this function represent?
(1) the additional charge for prep and gas
(2) the hourly rate she charges
(3) the number of hours she tutors
(1) the additional charge for prep and gas
Find the slope of the line that includes the following points.
(-12, -9) and (-3, -3)
-6/-9 = 6/9 = 2/3
Graph the following line.
2x + 3y = 21
1. Start by putting in slope-intercept form
y = -2/3x + 7
2. y-intercept is at (0, 7)
3. Down 2, right 3
Rewrite the following equation in slope-intercept form.
3.5x - 7y = 21
-7y = -3.5x + 21
y = 1/2x - 3
Given the following two points of a line, find the slope and then find the y-intercept.
(15, -10) and (5, 10)
slope = -2
y-intercept = 20
(equation would be y = -2x + 20)
A hot air balloon tracks its height above the ground as a function of the time it has been rising. The relationship is given by the equation h = 4.25t + 14, where h is the height in feet and t is the time since it began to rise in seconds. Explain in context, the meaning of 4.25 and the meaning of 14.
(Include units AND what is happening)
The balloon is rising 4.25 feet per second.
The balloon started at 14 feet high.