Linear · Capstone · C1

Pick the method.

Everything together: read forms and intercepts, write equations from points, and solve systems by graphing, substitution, or elimination — choosing the cleanest path.

01 / THE IDEA

See it work.

Watch the method

Pick the method

Identify what’s asked, then apply the right tool.

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{y=x+1y=−x+5\begin{cases} y = x + 1 \\ y = -x + 5 \end{cases}
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1

The system

Two lines — the solution is the point on both.

y=x+1;  y=−x+5y = x + 1;\; y = -x + 5
2

Substitute one equation into the other

Solve for x, then back-substitute for y.

x=2x = 2
3

The solution

Write the intersection point.

(2,3)(2, 3)
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type (x, y).

streak 0
best 0
-8-888
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Answer:
— / WHY IT WORKS

The idea underneath.

The toolkit

Forms (m, b), intercepts, writing equations, and three system methods — pick what fits.

Why it works

Read first, then choose.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Solve: y=2x+9;y=x+7

1

The system

Two lines — the solution is the point on both. y = 2x + 9;\; y = x + 7

2

Substitute one equation into the other

Solve for x, then back-substitute for y. x = -2

3

The solution

Write the intersection point. (-2, 5)

EX 2medium

Solve: (1,-3)-(3,-7)

1

Find the slope

Slope = rise ÷ run between the points. m = -2

2

Find b, then write it

Use a point to find b, then write y = mx + b. y = -2x - 1

EX 3hard

Solve: y=-3x+6

1

Read m and b

In y = mx + b, m is the slope and b is the y-intercept. m = -3,\; b = 6

04 / COMMON TRAPS

Where students slip.

Trap

Confusing slope with intercept.

Fix

m is steepness; b is where it crosses.

Trap

Picking a clumsy method.

Fix

Use the easiest for the given form.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Solve: y=x-2

Need a hint?
  • Identify the task.
  • Apply the matching method.
C2

Solve: y=3x-3

Need a hint?
  • Identify the task.
  • Apply the matching method.
C3

Solve: y=-3x+5

Need a hint?
  • Identify the task.
  • Apply the matching method.
C4

Solve: y=-2x+11;y=-x+7

Need a hint?
  • Identify the task.
  • Apply the matching method.
Apply

Apply (4)

A1

Solve: (-3,-2)-(-2,0)

Need a hint?
  • Identify the task.
  • Apply the matching method.
A2

Solve: y=2x-5

Need a hint?
  • Identify the task.
  • Apply the matching method.
A3

Solve: y=3x-4

Need a hint?
  • Identify the task.
  • Apply the matching method.
A4

Solve: (0,3)-(3,9)

Need a hint?
  • Identify the task.
  • Apply the matching method.
Extension

Extension (4)

E1

Solve: y=x-1;y=-3x+7

Need a hint?
  • Identify the task.
  • Apply the matching method.
E2

Solve: y=-x+6

Need a hint?
  • Identify the task.
  • Apply the matching method.
E3

Solve: (-1,4)-(2,-2)

Need a hint?
  • Identify the task.
  • Apply the matching method.
E4

Solve: y=-2x+6;y=x+0

Need a hint?
  • Identify the task.
  • Apply the matching method.