Finding Slope of a Line
What does the "m" value in the slope-intercept form represent? Explain.
It is the slope of the line. We use it to find a second point when graphing a line by hand. It is the rise over run value used after we graph the y-intercept.
What form do we use to graph a linear equation by hand or using the calculator?
the slope-intercept form y = mx + b
What are the four types of slopes?
positive, negative, zero (horizontal line), and undefined slope or no slope (vertical line)
What are the two keys things you need to write the equation of a line?
slope and y-intercept
What are the three methods we learned to graph the equation of a line?
1.) Table of values
2.) Intercepts (x-intercept & y-intercept)
3.) Using the m and b value
What quadrant is the ordered pair (-9, -4) located?
Is (0, -4) in the same quadrant?
The ordered pair (-9, -4) located in Q3. The ordered pair (0, -4) is not in a quadrant, it is located on the y-axis.
Write an equation for a vertical line through the point (-3, 3)
x = -3
Name three ways to describe slope.
Possible answers:
rate of change
rise over run
(y - y)/(x - x)
change in y divided by the change in x
Graph the following equation using a table of values. Include at least 3 points. y = 1/3x + 4
(-3 , 3)
(0, 4)
(3, 5)
What is the slope of this equation?
x = 5
Undefined Slope
Write an equation for a line with the following slope and points.
m = 2/3 and (0, -2), (3, 0)
y = 2/3x - 2
Graph the following linear equation by finding the intercepts.
2x + 10 y = 20
Step 1: Plug zero in for x, and solve for y. You get the ordered pair (0, 2), that is the y-intercept.
Step 2: Plug zero in for y, and solve for x. You the ordered pair (10, 0)
Step 3: Plot the ordered pairs (0,2) and (10, 0) and connect them.
Explain how you would graph the following equation once it is in slope-intercept form.
8x + 4y = 16
Should be rewritten as y = -2x + 4 and then graphed by started on 4 on the y-axis and then going down 2 and over 1 to find a second point.
Write an equation for a line with the following two points. Find the slope and y intercept. (15, -10) (5, 10)
slope = -2 y intercept = 20
y = -2x + 20
Find the slope of the line that includes the following points. (-12, -9) (-3, -3). Does the line increase or decrease?
-6/-9 = 6/9 = 2/3
Increase because the slope is positive.
Explain how you would graph the equation
y = 1/2x -5 using the slope and y-intercept.
Start by plotting the y-intercept. Put a point on -5 on the y-axis. Then from that point use the slope which says to rise 1 up and run 2 forward. That would identify a second point on the line. Connect the y-intercept point to that new point.
Find the slope and y-intercept for the equation
2x + 10y = 20
First get the equation into y = mx + b form. Subtract 2x from both sides and then divide everything by 10. The equation would be y=-1/5x+2. The slope is -1/5 and the y-intercept is (0, 2).
Is x = 2 a solution to the equation 2(x - 5) + 3 = 13 ?
No it is not a solution. When the value 2 is substituted into the equation is does not produce a true statement.
The amount y(in dollars) of money you have left after playing x games at a carnival is y = -0.75x + 10. How much money do you have after playing eight games?
y = -0.75(8) + 10 y = -6 + 10 y = 4 $4 dollars left after playing 8 games. Graph should begin at (0, 10) on the y-axis and move down three and four to the right.