What is the equation of the line that passes through the point (2.75, 0.975) and has an x-intercept of 2 ?
A. y + 5.9 = 2.5x
B. 4y + 12x = 29.1
C. 6y + 27.15 = 12x
D. 10y - 13x = -26
Answer:D
What is the equation of the line that passes through the point (2.75, 0.975) and has an x-intercept of 2 ?
A. y + 5.9 = 2.5x B. 4y + 12x = 29.1 C. 6y + 27.15 = 12x D. 10y - 13x = -26
Explanation: D Plugging in the given point to see which equation is true is not easy on this one, since both values have weird decimals. The answer choices are also likely written so that more than one is true for that point, so try to find another point on the line. The x-intercept of a line is where the line crosses the x-axis. At that point, the value of y is 0. Therefore, (2, 0) is also a point on the line. Plug this point into the answers, since it is easier to calculate. If it works in more than one equation, plugging in the ugly point will determine the correct answer, which must work for both points work. Plug point (2, 0) into (A) to get 0 + 5.9 = 2.5(2). Solve both sides of the equation to get 5.9 = 5. Eliminate (A). Plug (2, 0) into (B) to get 4(0) + 12(2) = 29.1. Solve both sides of the equation to get 4 + 24 = 29.1, or 28 = 29.1. Eliminate (B). Plug (2, 0) into (C) to get 6(0) + 27.15 = 12(2). Solve both sides of the equation to get 0 + 27.15 = 24. Since this is clearly not a true statement, eliminate (C). Plug (2, 0) into (D) to get 10(0) - 13(2) = -26. Solve both sides of the equation to get -26 = -26. Since (D) is the only answer for which the point (2, 0) works, the correct answer is (D).