In the figure shown below, x and y are greater than or equal to 0, the vertices of triangle ABC have coordinate values as shown, and the value of AC is as shown. If x = 3, then what could be the equation of line AC?
A. 4x + 3y = 8
B. 3x - 4y = 8
C. 4x - 3y = 8
D. 4x + 3y = 24
E. 3x + 4y = 24
Since x=3, AB = (x+3) - x = (3+3) - 3 = 3.
Thus, ∆ABC is a 3-4-5 triangle.
Since AB=4, the y-intecept of line AC must be greater than 4.
The x-coordinate of any y-intercept is 0.
Thus, when x=0 is plugged into the correct answer choice, the resulting y value must be greater than 4.
A quick scan of the answer choices reveals that only D and E are viable.
Eliminate A, B and C.
To travel from point A to point C, we move down 4 units and to the right 3 units, implying a slope of -4/3.
Answer choice
D:
4x + 3y = 24
3y = -4x + 24
y = (-4/3)x + 8.
Success! The slope = -4/3.
The correct answer is
D.
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