The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c² = a² + b² or, solved for c, \(c = \sqrt{a + b}\)

An equation is two expressions separated by an equal sign. The key to solving equations is to repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.

A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).

The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, -2) and (2, -4) so the slope becomes:

You need to find the value of a so solve the first equation in terms of y:

-4a + y = 1
y = 1 + 4a

then substitute the result (1 - -4a) into the second equation:

-7a + 3(1 + 4a) = 5
-7a + (3 x 1) + (3 x 4a) = 5
-7a + 3 + 12a = 5
-7a + 12a = 5 - 3
5a = 2
a = \( \frac{2}{5} \)
a = \(\frac{2}{5}\)