Work with equations of the form Ax + By = C, including finding intercepts and interpreting graphs of lines.
26 original linear equations in two variables questions in the SAT Ranker bank, with instant scoring and an Elo-based rank once you sign up. Below are a few free samples with full explanations.
A line is defined by the equation 7x + 6y = 42. What is the line's x-intercept (the x-value where y = 0)?
Setting y = 0 leaves 7x = 42. The answer is 6. 7 finds the y-intercept instead, by setting x to 0; 42 stops at 42 without dividing by the coefficient; -6 drops a sign when rearranging.
A line is defined by the equation 7x + 11y = 77. What is the line's x-intercept (the x-value where y = 0)?
Setting y = 0 leaves 7x = 77. The answer is 11. 7 finds the y-intercept instead, by setting x to 0; 77 stops at 77 without dividing by the coefficient; -11 drops a sign when rearranging.
A line is defined by the equation 8x + 6y = 72. What is the line's y-intercept (the y-value where x = 0)?
Setting x = 0 leaves 6y = 72. The answer is 12. 9 finds the x-intercept instead, by setting y to 0; 72 stops at 72 without dividing by the coefficient; -12 drops a sign when rearranging.
A line is defined by the equation 3x + 7y = 21. What is the line's y-intercept (the y-value where x = 0)?
Setting x = 0 leaves 7y = 21. The answer is 3. 7 finds the x-intercept instead, by setting y to 0; 21 stops at 21 without dividing by the coefficient; -3 drops a sign when rearranging.
A line in the xy-plane passes through the point (0, 4) and has a slope of 3. What is the equation of the line?
In slope-intercept form y = mx + b, the slope m is 3 and the y-intercept b is 4 (the point where x = 0), giving y = 3x + 4. Choice y = 4x + 3 swaps the slope and intercept.