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Points B and C are on the line y = 2x + 3. Point A is the y-intercept of the line. If AB = AC, what is the relationship between A, B, and C?

Mathematics

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Graph of y = 2x + 3

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Key points of y = 2x + 3
Pointxy
x-intercept−1.50
y-intercept03

Step-by-step solution

2 steps

Here's a step-by-step solution to the problem:

  1. Find the coordinates of point A.

    Point A is the y-intercept of the line y=2x+3y = 2x + 3. To find the y-intercept, we set x=0x = 0.

    y=2(0)+3y = 2(0) + 3 y=3y = 3

    So, the coordinates of point A are (0,3)(0, 3).

  2. Determine the relationship between A, B, and C.

    Points B and C are on the line y=2x+3y = 2x + 3. The condition AB=ACAB = AC means that point A is the midpoint of the line segment BC, because A, B, and C

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