Reach for the Star

Straight line equations · Optional extension

L042 · Allow 10–15 minutes for learners ready to move on. Answers are available after an attempt.

Stretch

Find the equation of the line through (2,−1) and (6,7).

Reveal a worked check after attempting

m=2; −1=2(2)+c gives c=−5, so y=2x−5.

Deep challenge

The lines y=3x−4 and 6x−2y=8 are claimed to intersect. Test the claim.

Reveal a worked check after attempting

Rearranging the second gives y=3x−4; they are the same line, so there is no single intersection.

Recall & Review: feedback and extension integration

Lesson L042: Straight line equations

Objective: Form and use straight-line equations and locate intersections.

60-minute structure: 0-7 Connect & Check; 7-14 Share; 14-25 Present/model; 25-44 Apply route choice/practice; 44-52 independent exam-style check; 52-60 Recall & Review, WWW/EBI and next step.

What Went Well (WWW)

I represented the algebraic structure accurately, kept each transformation valid and checked the result by substitution, graph or equivalent reasoning.

Even Better If (EBI)

I will show the missing inverse operation or algebraic step, keep signs and brackets accurate and test the result in the original relationship.

Stretch and deep challenge

Stretch: Find the equation of the line through (2,−1) and (6,7).

Deep challenge: The lines y=3x−4 and 6x−2y=8 are claimed to intersect. Test the claim.