➕ Algebra 1 · Linear Functions
Standard Form of a Line flashcards
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All 14 flashcards at a glance
Card 1
What is standard form of a line?
Ax + By = C, with A and B not both 0. The x term and the y term are on the left, and a number is on the right.
Card 2
Name A, B and C in x − 8y = 16.
A = 1 (the x has an invisible 1), B = −8 (the minus sign stays with the 8), C = 16.
Card 3
Find both intercepts of 7x − 6y = 42.
Cover −6y: 7x = 42, so x = 6, and the line crosses at (6, 0). Cover 7x: −6y = 42, so y = −7, and the line crosses at (0, −7).
Card 4
Why does covering the y term give the x-intercept?
Every point on the x-axis has y = 0, so the y term becomes 0. What is left, Ax = C, gives the x-value where the line crosses the x-axis.
Card 5
Write x + 4y = 20 in slope-intercept form.
Subtract x: 4y = −x + 20. Divide every term by 4: y = −(1/4)x + 5.
Card 6
Write y = 4x − 3 in standard form.
Subtract 4x: −4x + y = −3. Then multiply every term by −1 so A is not negative: 4x − y = 3.
Card 7
Write (1/3)x − (1/2)y = 5 with integers.
Multiply every term by 6: 2x − 3y = 30.
Card 8
What kind of line is 5y = −20?
Here A = 0. Dividing by 5 gives y = −4: a horizontal line with slope 0.
Card 9
What kind of line is 2x = 14?
Here B = 0. Dividing by 2 gives x = 7: a vertical line with an undefined slope.
Card 10
What are the slope and y-intercept of Ax + By = C (with B ≠ 0)?
The slope is −A/B and the y-intercept is C/B. Both come from solving for y: y = −(A/B)x + C/B.
Card 11
In this lesson’s WAT trick for tidy standard form, what do W, A and T stand for?
W: without fractions or decimals (A, B and C are integers). A: A is not negative. T: trimmed, meaning no common factor. It is a convention, not a law.
Card 12
Pens cost 2 dollars and notebooks cost 5 dollars. Write an equation for spending exactly 40 dollars on p pens and n notebooks, and name the intercepts.
2p + 5n = 40. All pens: p = 20, the point (20, 0). All notebooks: n = 8, the point (0, 8).
Card 13
Is (−2, 5) on the line 4x − 3y = −23?
Substitute: 4(−2) − 3(5) = −8 − 15 = −23. Both sides match, so yes.
Card 14
Is 10x + 15y = 30 in the usual standard form?
No: 10, 15 and 30 share the common factor 5. Dividing every term by 5 gives 2x + 3y = 6, which is the same line in the usual form.