➕ Algebra 1 · Linear Functions
Standard Form of a Line: true or false
Decide fast, then read the reason. Wrong answers are the best teachers, so every statement explains itself.
All statements and answers
In 10x − 3y = 15, B = 3.
✗ False. The minus sign belongs to the 3, so B = −3. The equation means 10x + (−3)y = 15.
For Ax + By = C with B ≠ 0, the y-intercept is C/B.
✓ True. Cover the x term to get By = C, so y = C/B. The line crosses the y-axis at (0, C/B).
The equations 20x − 10y = 50 and 2x − y = 5 have the same graph.
✓ True. Dividing every term of the first equation by 10 gives the second, and that does not change which points make it true.
The rule that A must not be negative is a convention, not a law of math.
✓ True. −x + 4y = 8 and x − 4y = −8 have the same graph. The convention just picks one tidy version.
To find the x-intercept of a line, set x = 0.
✗ False. The x-intercept is where the line crosses the x-axis, where y = 0. Setting x = 0 finds the y-intercept.
The x-intercept of 9x + 5y = 45 is 9.
✗ False. Cover the y term: 9x = 45, so x = 5. The x-intercept is 5. The number 9 is the y-intercept: cover the x term to get 5y = 45, so y = 9.
The graph of 4y = 20 is a vertical line.
✗ False. Dividing by 4 gives y = 5. Every point has y = 5, so the line is horizontal.
The line 6x = −30 has slope 0.
✗ False. Dividing by 6 gives x = −5, a vertical line. Its slope is undefined, not 0.
The slope of Ax + By = C (with B ≠ 0) is A/B.
✗ False. Solving for y gives y = −(A/B)x + C/B, so the slope is −A/B.
The line 5x − 2y = 0 passes through the origin.
✓ True. At (0, 0), 5(0) − 2(0) = 0, which matches the right side.
By the usual convention, −x + 4y = 8 is rewritten as x − 4y = −8.
✓ True. A = −1 is negative, so multiply every term by −1. The line stays the same.
Every line, including a vertical line, can be written in the form Ax + By = C.
✓ True. A vertical line x = 3 is 1x + 0y = 3, and a horizontal line y = 3 is 0x + 1y = 3.