Slope-Intercept Form
What is the slope of the line that passes through the points (4, 3) and (12, -1)?
m = (y2 - y1)/(x2 - x1)
m = (-1 -3)/(12 - 4)
m = -4/8
ANSWER: m = slope = -1/2
How many solutions does the following function have?
2(3x + 10) = 6x - 15
1. 2(3x + 10) = 6x - 15
2. 6x + 20 = 6x - 15
Same Coefficient (slope)
Different Constant (y-intercept)
ANSWER: No Solutions
Convert the following function from Standard form to slope-intercept form:
-20x + 5y = 10
1. -20x + 5y = 10
2. ADD 20x from Both Sides
-20x + 5y = 10
5y = 10 + 20x
3. DIVIDE BOTH SIDES BY 6
5y = 10 + 20x
y = 2 + 4x
ANSWER: y = 4x + 2
Solve the following system of equations:
y = 6x + 5
y = -2x + 13
6x + 5 = -2x + 13
1. ADD 2x to Both Sides
8x + 5 = 13
2. SUBTRACT 5 from Both Sides
8x = 8
3. Divide by 8 on Both Sides
x = 1
4. Substitute and Solve for y
y = 6x + 5
y = 6(1) + 5
y = 6 + 5 = 11
ANSWER: x = 1 y = 11
Simplify the following exponential expression
p10 * p7 * p4
ANSWER: p21
When multiplying with exponents, keep the base and add the exponents.
Convert the following function from Standard form to slope-intercept form:
6x + 2y = 14
1. 6x + 2y = 14
2. SUBTRACT 6x from Both Sides
6x + 2y = 14
2y = 14 - 6x
3. DIVIDE BOTH SIDES BY 2
2y = 14 - 6x
y = 7 - 3x
ANSWER: y = -3x + 7
Which of the following tables (in Desmos) does NOT represent a function?
a) Table A
b) Table B
c) Table C
ANSWER: Table A (a)
Table A does not represent a function because a function is when x does not repeat or each input has only one output. In table A the x-value of -3 repeats or shows up more than once, so table A is not a function.
What is the slope of the following table (in Desmos)?
Change in y = -11
Change in x = 4
ANSWER: m = slope = -11/4
Which of the following regions represents the solution set of the system of inequalities seen on the graph (in Desmos)?
ANSWER: Region C
The double-shaded or cross-shaded region
Simplify the following expression:
Square root of 18
ANSWER: 3 times the square root of 2
Square Root of 18 =
Square Root of 9 times Square Root of 2 =
3 times Square Root of 2
Annotate the slope (positive or negative) and y-intercept (positive or negative) of the red graph (in Desmos).
Slope = Negative (downhill)
Y-Intercept = Positive (starts in middle on y-axis above origin)
Find f(1)
x = 1 (inside parentheses)
y = (x - 4)^2 + 20
y = (1 -4)^2 + 20
y = (-3)^2 + 20
y = (-3)(-3) + 20
y = 9 + 20
y = 29
ANSWER: f(1) = 29
Write an equation of a line parallel to
y = 3/7x + 2
that passes through the point (0,6)
ANSWER: y = 3/7x + 6
Parallel Lines have the Same Slope, Different Y-Intercepts
m = slope = 3/7
b = y-intercept = (0,6) = 6
Is the following set of lines parallel, perpendicular or neither? Explain how you know.
y = 3/5x - 7
y = 3/5x + 2
ANSWER: The 2 lines are PARALLEL because they have the SAME SLOPE and DIFFERENT Y-INTERCEPTS.
If 5x + 7 = 62, what is the value of 3x?
5x + 7 = 62
1. Subtract 7 from Both Sides
5x + 7 = 62
5x = 55
2. Divide Both Sides by 5
5x = 55
x = 11
3. Answer Question
3x = ?
3(11) = 33
ANSWER: 33
Which of the following equations best represents the blue line (in Desmos)?
a) y = 2/3x + 1
b) y= 2/3x + 6
c) y = 3/2x - 5
d) y = 3/2x + 6
Answer:
2 Points:
Point 1: (0,6) = y-intercept
Point 2: (3, 8)
m = slope = 2/3
b = y-intercept = 6
ANSWER: b (y = 2/3x + 6)
Mr. Simmons is only allowed to tell 8 bad dad jokes a class, which earn an unlimited amount of groans from students. If j represents the number of dad jokes Mr. Simmons tells each day and g(j) represents the number of groans he receives, which of the following best represents the domain of the function?
a) All Rational Numbers
b) All Integers
c) All Positive Integers
d) All Positive Integers Up To 8
domain = x-values
x = j (inside parentheses) = number of dad jokes
1. Can dad jokes be negative? NO
2. Can dad jokes be a fraction? NO
3. Can dad jokes be zero? YES
d) Does dad jokes have a min/max? MAX of 8
ANSWER: D (All Positive Integers Up To 8)
Write an equation of a line perpendicular to
y = 3/7x + 2
ANSWER: y = -7/3x + 2
Perpendicular Lines have opposite reciprocal slopes.
Original m (slope) = 3/7
Perpendicular m (slope) = -7/3
Which of the following graphs best represents the system of inequalities (in Desmos)?
ANSWER: Graph A
Line 1 (Red): >= (Solid/Shaded Above)
Positive Slope, Negative Y-Intercept
Line 2 (Blue): < (Dotted/Shaded Below)
Negative Slope, Positive Y-Intercept
Identify all 3 (x,y) coordinates of the labeled points on the purple line (in Desmos)
Point A: (-2, 9)
Point B: (0, 5)
Point C: (4,-3)
Write a slope-intercept equation for the orange graph seen on the screen (in Desmos)
Point 1: (0,-5) = y-intercept
Point 2: (3, -4)
m = slope = 1/3
b = y-intercept = -5
ANSWER: y = 1/3x - 5
Which of the following inequalities best represents the function seen in the graph (in Desmos)?
a) y < -2x - 3
b) y > -2x - 3
c) y >= -2x - 3
d) y > -2x + 3
ANNOTATIONS:
Negative Slope (downhill)
Negative Y-Intercept (starts in middle on y-axis below origin)
Dotted Line, Shaded Above: > (Greater Than)
ANSWER: B (y > -2x - 3)
In slope-intercept form, write the equation of a line that passes through the points (-1, 10) and (3, 2).
1. m = slope = (2 - 10)/(3 - -1) = -8/4 = -2
2. m = -2 (-1,10) x = -1 y = 10
y = mx + b
10 = -2(-1) + b
10 = 2 + b
8 = b
3. m = -2 b = 8
ANSWER: y = -2x + 8
Solve the following system of equations
4x + 3y = 2
3x + 2y = 3
Method (Elimination)
Least Common Multiple: 12x
Multiply Equation 1 by 3 (Get 12x)
Multiply Equation 2 by -4 (Get -12x)
ANSWER: x = 5 y = -6
Simplify the following expression:
Square Root of 300 minus Square Root of 48
ANSWER: 6 times the square root of 3