SAT Math Multiple Choice Question 190: Answer and Explanation
10. Line d has a slope of and passes through the point (1, 1). Line e is parallel to line d and has a y-intercept 3 times that of line d. Which of the following is the equation of line e ?
- A. 5y - 4x = 3
- B. 5y - x = 4
- C. 10y - 8x = 30
- D. 20y + 25x = 12
Correct Answer: A
A The equation of a line expressed in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. One way to find the y-intercept of line d is to plug in the slope and given point and slope for b. The equation y = mx + b becomes 1 = (1) + b. Subtract from both sides to get b = . Another approach is to use the slope formula to find b. The y-intercept of a line is where the line crosses the y-axis; at that point x = 0. Therefore, in addition to the point (1, 1), there is another point (0, b) that lies on line d. The equation for finding the slope of the line given two points is . Therefore = or = . Cross-multiply to get 5(b - 1) = -4. Distribute the 5 to get 5b - 5 = -4. Solve for b to get 5b = 1, and b = . The y-intercept of line e is 3 times , so the y-intercept of line e is . Additionally, parallel lines have slopes that are equal to each other. Therefore, line e will also have a slope equal to . Rewrite the equation in (A) in the slope-intercept form of the equation to get 5y = 4x +3, or y = x + . The slope of this line is and the y intercept is . Therefore, the correct answer is (A).