➕ Algebra 1 · Linear Functions

Graphing Linear Equations: true or false

Decide fast, then read the reason. Wrong answers are the best teachers, so every statement explains itself.

All statements and answers

• The point (2, 10) is on the graph of y = 3x + 4.

  ✓ True. Substitute: 3(2) + 4 = 10, which matches the y-coordinate.

• A slope of 2/5 means that going up 2 and right 5 from a point on the line leads to another point on the line.

  ✓ True. Slope is rise over run, so a rise of 2 and a run of 5 stays on the line.

• The line x = −3 is horizontal.

  ✗ False. Every point on x = −3 has x-coordinate −3, so the line is vertical. A horizontal line looks like y = a number.

• The line y = 6 has slope 0.

  ✓ True. The y-value never changes, so the rise is 0 and the slope is 0.

• You need at least ten points to draw a line accurately.

  ✗ False. Exactly one straight line passes through two different points. Use a third point as a check.

• A line with slope −1/2 through (0, 3) also passes through (2, 4).

  ✗ False. A negative slope goes down as you move right: down 1 and right 2 from (0, 3) gives (2, 2). The point (2, 4) would need slope +1/2.

• The x-intercept of 5x + 4y = 20 is 5.

  ✗ False. For the x-intercept set y = 0: 5x = 20, so the x-intercept is 4 (the point (4, 0)). The number 5 is the y-intercept: setting x = 0 gives 4y = 20, so y = 5.

• Every line crosses both the x-axis and the y-axis.

  ✗ False. The horizontal line y = 3 never meets the x-axis, and the vertical line x = 3 never meets the y-axis.

• The point (5, 9) is on the graph of y = 2x + 1.

  ✗ False. Substitute x = 5: 2(5) + 1 = 11, not 9. The point is near the line, but near is not on.

• The graph of y = 3x passes through the origin.

  ✓ True. When x = 0, y = 3(0) = 0, so (0, 0) is on the line.

• The point (3, −2) is 3 units to the right of the y-axis and 2 units below the x-axis.

  ✓ True. The first number is the horizontal move (right 3) and the second is the vertical move (down 2).

• If a table of values for a line shows y going up by 4 each time x goes up by 1, the slope is 4.

  ✓ True. Slope is rise over run: 4/1 = 4.