MATH 130 · Review R.6 · Sections 1.1, 1.2, 1.4

Linear Equations and Lines

Solve, rearrange, interpret slope, and write line equations

50–55 minutes · Offline capable · Quiz 2 · Sep 9 at 2:10 PM

Learning roadmap and pacing

  1. 1

    solve linear equations and identify special cases

  2. 2

    rearrange formulas for a specified variable

  3. 3

    interpret slope from points, equations, and context

  4. 4

    write parallel and perpendicular line equations

Canvas pacing anchor

Quiz 2 · Sep 9 at 2:10 PM

ALEKS Review R.6 and Sections 1.1, 1.2, 1.4 due Sep 9 at 2:10 PM

Coverage note

This deck is the sequential study path. Official quiz and test coverage can be adjusted in Canvas or in class.

Activate · 2 minUnit 1 sequence

Entrance retrieval

4 minutes · no notes
  1. Solve $-9x+26=-4(x-9)$.
  2. Find the slope through $(8,-8)$ and $(1,16)$.
  3. What slope is perpendicular to $3$?

Activate · 4 minUnit 1 sequence

Linear equations: preserve equivalence

1

Distribute and clear grouping symbols.

2

Combine like terms on each side.

3

Move variable terms, then constants.

4

Divide and substitute back.

Special cases

$0=0$ means all real numbers; a false statement such as $0=5$ means no solution.

Explain · 5 minUnit 1 sequence

Literal equations: isolate the target

Solve $A=P+Prt$ for $r$.

  1. Subtract $P$: $A-P=Prt$.
  2. Divide by every factor attached to $r$.
  3. $r=\dfrac{A-P}{Pt}$.

Model · 5 minUnit 1 sequence

Slope connects change to an equation

$m=\dfrac{y_2-y_1}{x_2-x_1}$

Use one consistent point order. Units are “change in output per one unit of input.”

$y=mx+b$: read $m$ and intercept quickly.

$y-y_1=m(x-x_1)$: write from a point and a slope.

Explain · 5 minUnit 1 sequence

Model: write a line from two points

Use $A(8,-8)$ and $B(1,16)$.

  1. $m=(16-(-8))/(1-8)=-24/7$.
  2. Point-slope: $y+8=-\frac{24}{7}(x-8)$.
  3. Check both original points in the equation.

Model · 6 minUnit 1 sequence

Parallel and perpendicular are slope decisions

Parallel

Same slope. Through $(-6,2)$ parallel to $y=3x+3$: $y-2=3(x+6)$.

Perpendicular

Negative reciprocal. The perpendicular slope is $-1/3$.

Explain · 4 minUnit 1 sequence

You try: equation-to-line chain

Work first · then reveal

  1. Solve $-\frac12x-\frac43=\frac{7x-7}{3}$.
  2. Solve $d=rt$ for $t$.
  3. Write the line through $(2,-1)$ perpendicular to $y=\frac12x+4$.

Practice · 5 minUnit 1 sequence

Quiz 2 checkpoint: readiness check

Quiz 2 checkpoint
Closed notes · show complete work
  1. Solve $4(2x-3)=5x+9$ and check.
  2. Solve $V=\frac13Bh$ for $h$.
  3. Find the slope through $(-2,5)$ and $(4,-7)$.
  4. Write the parallel line through $(1,4)$ to $2x+y=6$.

Assess · 8 minUnit 1 sequence

Exit ticket and next step

Before you leave
  1. Name one skill you can now complete without notes.
  2. Name one error pattern to watch.
  3. Schedule the next short practice before the checkpoint.
Next step

Next: Unit 1C — functions, domain and range, and coordinate geometry

Synthesize · 3 minUnit 1 sequence