Mike correctly found the slope and y intercept of the line passing through the points(-5,-2)and (3,14)as follows.
9, 40 and 41
all right triangle have lengths that follow the pythagorean theorem (a²+b² = c²). right triangles have one angle equal to 90°. the two shorter sides form the right angle and the side opposite the right angle is called the hypotenuse.
using the lengths given, we can use guess and check to see what sum of two sides squared would equal a third side, or just plug them into the equation: a²+b² = c² and see what lengths fit this equation.
i recommend starting with squares you are familiar with:
9² + 40²= 81 + 1600 = 1681
now, take the √1681 to find the length of 'c', or the hypotenuse:
√1681 = 41
since these three lengths fit the pythagorean theoreom, the would form a right triangle.
y = -4
we are given the following equation and we are to find the value of y when x equals to 6:
substituting the given value of x in the above equation:
therefore, y = -4 when x = 6.
let's have in mind:
f(n) = a1 + (n - 1).r
r = a2 - a1
r = 10 - 3
r = 7
f(n) = a1 + (n - 1).7
f(n) = 3 + (n - 1).7
f(n) = 3 + 7n - 7
f(n) = 7n - 4