Linear Functions • Topic 7 of 7

Standard Form

Standard form of a line is Ax + By = C, with A, B and C usually integers. It is convenient for finding intercepts quickly: set y = 0 to get the x-intercept (x = C/A) and x = 0 to get the y-intercept (y = C/B). To convert to slope-intercept form, solve for y; the slope is −A/B. Standard form is common in systems of equations and in problems stated as "Ax + By = C." Being able to move fluently between standard and slope-intercept form lets you read intercepts or slope, whichever a question needs.

✅ Solved examples

1. Find the x-intercept of 2x + 3y = 12.
Set y = 0: 2x = 12 → x = 6. The x-intercept is (6, 0).
2. Find the y-intercept of 2x + 3y = 12.
Set x = 0: 3y = 12 → y = 4. The y-intercept is (0, 4).
3. What is the slope of 4x + 2y = 10?
Slope = −A/B = −4/2 = −2.
4. Convert 3x + y = 6 to slope-intercept form.
Subtract 3x: y = −3x + 6.

✏️ Practice — try these, take hints as needed

1. Find the x-intercept of 5x + 2y = 20.
Set y = 0.
5x = 20.
Solve for x.
(4, 0).
2. Find the y-intercept of 5x + 2y = 20.
Set x = 0.
2y = 20.
Solve for y.
(0, 10).
3. What is the slope of 6x + 3y = 9?
Slope = −A/B.
−6/3.
—
−2.
4. Convert 2x + y = 7 to slope-intercept form.
Subtract 2x.
y = −2x + 7.
—
y = −2x + 7.
5. Find the x-intercept of x − 4y = 8.
Set y = 0.
x = 8.
—
(8, 0).

📝 Topic test — 8 questions

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