Writing & Solving Equations ✏️
Turn words into equations, solve for x, and discover the three types of solutions. Standard 8.EE.C.7
0%
L1
Writing Equations from Words 📝
Turning language into algebra
Question 1 of 3
A number is four more than three times another number. The larger number is 19. Write an equation where x is the smaller number.
Question 2 of 3
The sum of two consecutive integers is 47. Let x be the smaller integer. Write the equation.
Question 3 of 3
Which of these are linear expressions in x? Tap all that apply! 👇
5x + 3
x² + 2
7x − 1
1/x
−4x
L2
Solving Linear Equations 🔧
Properties of equality, step by step
Question 1 of 4
Solve: x + 13 = 27
x =
Question 2 of 4
Solve: 4x − 7 = 29
x =
Question 3 of 4
Solve: 2(3x + 5) = 28
💡 Expand 2(3x + 5) first using the distributive property, then solve.
x =
Question 4 of 4
Solve: 5x + 3 = 2x + 18
x =
L3
Classification Challenge 🏆
One / none / infinitely many solutions
Question 1 of 3
3x + 9 = 3(x + 3)
Expand the right side. What kind of equation is this?
♾️ Infinitely many
1️⃣ One solution
🚫 No solution
Question 2 of 3
2x + 5 = 2x + 11
♾️ Infinitely many
1️⃣ One solution
🚫 No solution
Question 3 of 3
7x − 4 = 3x + 16
♾️ Infinitely many
1️⃣ One solution
🚫 No solution
Two Variables & Graphs 📈
Tables of solutions, coordinate plane graphing, proportional relationships. Standard 8.EE.B.5
0%
L4
Paul's Walk — Constant Rate 🚶
Proportional relationships & equations in two variables
Question 1 of 3
Paul walks 2 miles in 25 minutes. His equation is y = 0.08x (x = mins, y = miles). How many miles can he walk in 100 minutes?
miles
Question 2 of 3
Maria walks 3 miles in 45 minutes. What is her speed in miles per minute? Write as a decimal.
Question 3 of 3
Paul walks at 0.08 mi/min, Maria at 0.067 mi/min. The slope of the graph equals the speed. Who is faster?
🏃 Paul is faster
🏃 Maria is faster
🤝 Same speed
L5
Graph Explorer — y = mx + b 🎮
Table, graph & equation all in sync
1
0
y = 1x + 0
Quick challenge 🎯
Set slope = 2 and intercept = −3 using the sliders above. What is y when x = 4?
y =
Slope & Equations of Lines 📐
Steepness, rise over run, slope formula, y = mx + b. Standards 8.EE.B.5–6
0%
L6
Slope Explorer 🎢
Rise, run, and the steepness of a line
2
1
Rise
2
Run
1
Slope
2.00
Question 1 of 2
Using m = (y₂ − y₁) / (x₂ − x₁), find the slope through the points (1, 3) and (4, 9).
m =
Question 2 of 2
A line has slope m = 3 and passes through the point (2, 7). Find the y-intercept b.
💡 Substitute x = 2, y = 7, m = 3 into y = mx + b and solve for b.
b =
Simultaneous Equations 🎯
Two equations, one solution — graphically and by substitution. Standard 8.EE.C.8
0%
L7
Derek's Basketball Problem 🏀
Introduction to simultaneous equations
Question 1 of 2
Derek scored 30 points with two-point and three-point shots, making 5 more two-pointers than three-pointers. System: { 2x + 3y = 30 and x = y + 5 }. Find x (two-pointers).
x =
Question 2 of 2
Solve by substitution: { y = 3x + 1 and 2x + y = 16 }. Find x.
💡 Substitute y = 3x + 1 into 2x + y = 16 and solve for x.
x =
L8
Graphical Solution 📊
Find where two lines cross
🔴 Line 1
1
-2
🔵 Line 2
-1
4
Type
One solution
x
3.0
y
1.0