Solving Multi-Step Equations
Solving Equations
with Different Solutions
with Different Solutions
Similar Triangles
Solving Equations
Solving Equations
Slope / Rate of Change
Slope-Intercept Form
y=mx+b
y=mx+b
100
Solve for x: 3/4x + 6 = 60
3/4x = 54
x = 72
100
Match each equation on the left with its solution on the right.
a. No solution,
c. One solution,
b. Infinite solutions *ALERT*
100
Sides AC and DA of similar triangles ABC and DFA both lie on the line k. Find the slope of Line k.
HINT: don't forget to simplify!
m = 2/6
m = 1/3
100
Slope, also known as rate of change, is represented in linear equations by what variable(letter)?
m
(michael: m=y/x)
100
Write the equation of a line with slope -3/2 and y-intercept of 1
HINT: use y = mx + b
m = -3/2 b = 1
y = -3/2x + 1
200
Solve for x: 1/2x + 4 = 16
1/2x = 12
x = 24
200
State whether the solution to the following equation is one solution, infinite solutions, or no solution.
4x + 12 = 2x + 12 + 2x
Infinite Solutions *ALERT ALERT*
200
Triangle ABC is translated to create triangle DEF, as shown below. In these triangles, side AC is congruent to side DF. Determine the value of x by setting up an equation and solving it.
5(3x + 3) = 20x + 30
15x + 15 = 20x + 30
15 = 5x + 30
-15 = 5x
-3 = x
200
What is the rate of change (slope) of the equation: y = -x + 5 ?
m = -1
200
Write the equation of a line with slope -1 and y-intercept of -3
HINT: use y = mx + b
m = -1 b = -3
y = -x - 3
300
Solve for x: 10x - 5 + 4x = 79
14x - 5 = 79
14x = 84
x = 6
300
State whether the solution to the following equation is one solution, infinite solutions, or no solution.
3(x + 8) - x + 6 = 2(2x + 3) - 9
One solution
2x + 30 = 4x - 3
300
Triangle ABC is translated to create triangle DEF, as shown below. In these triangles, side AB is congruent to side DE. Determine the value of y by setting up an equation and solving it.
-14y - 18 = 2(12y + 10)
-14y - 18 = 24y + 20
-18 = 38y + 20
-38 = 38y
-1 = y
300
What is the slope (rate of change) of the graph shown
m = -2/3
300
Would the point (5, -5) lie on the line: y = -3x + 10 ?
HINT: use substitution
-5 = -3(5) + 10
-5 = -15 +10
-5 = -5
YES
400
Solve for x: 6x - 3 + 2x = 21
8x - 3 = 21
8x = 24
x = 3
400
Which value of x would result in INFINITE SOLUTIONS for the equation below?
x(3y - 2) = 6y - 4
x = 2
400
Triangle ABC is translated to create triangle DFG, as shown below. In these triangles, side AB is congruent to side DF. Determine the value of x by setting up an equation and solving it.
3(2x + 10) = 12x + 12
6x + 30 = 12x + 12
30 = 6x + 12
18 = 6x
3 = x
400
State whether the following graphs have positive, negative, zero, or undefined slopes
Positive, Zero, Negative, Undefined
400
Write the equation of the line shown in the graph
m = -2/3 b = 0
y = -2/3x
500
Solve for x: 1/3(6x - 12) = 3x + 6
2x - 4 = 3x + 6
-4 = 1x + 6
-10 = 1x
x = -10
500
Which value of x would result in NO SOLUTION for the equation below?
x(-10y + 6) = -30y - 4
x = 3
500
Triangle ABC is translated to create triangle DFG, as shown below. In these triangles, side BC is congruent to side FG. Determine the value of y by setting up an equation and solving it.
2y + 12 = 2(2y - 3)
2y + 12 = 4y - 6
12 = 2y - 6
18 = 2y
9 = y
500
Find the slope of a line that passes through (0, 5) and (4, 13)
HINT: use m = y2 - y1 / x2 - x1
m = 13 - 5 / 4 - 0
m = 8/4
m = 2
500
A line has a y-intercept of -4 and passes through the points (5, 9) and (6, 11). Find the slope and then write the equation of the line.
HINT: use m = y2 - y1 / x2 - x1
m = 11 - 9 / 6 - 5
m = 2/1
y = 2x - 4