Question

A circle representing a pool is graphed with a center at the origin. Grant enters the pool at point A and swims over to a friend who is located at point B.

A coordinate plane with a circle drawn. The center of the circle is the origin, (0, 0). The circle has a diameter of 16 units. There is a line segment drawn from Point A at (8, 0), passing through (0, 4) to Point B at (negative 4, 6).

Which equation represents Grant’s path?

y = 2 – 4x
y = 4 –
y = 6 –
y = 8 – 2x

Answer 1

clickable: https://us-static.z-dn.net/files/d6e/214672ad27a0dee3362a57e490271e08.png

Answer 2

the circle is actually unnecessary to solve this problem. to create a linear equation you simply need two of the points along AB.

let's use (8,0) and (0,4) to make the arithmetic easier. let's assign (x1,y1) to be (8,0) and (x2,y2) to be (0,4)

apply the slope formula

m = (y2-y1) / (x2-x1)

once you have m, you can use the equation y = mx + b, plug in one of the points from before to be your (x,y), and solve for the y-intercept (b)