Question

1. What is the intercept (y-intercept) of the function y = 2.5x + 8
is it 8?

2. What is the x-intercept of the function y = 2.5x + 8
i'm honestly not sure...

3. What is the slope of the function y = 2.5x + 8
um...is it 2.5?

4. The sides of a triangle are 6,10, and 12. Using Pythagorean Theorem, determine if the triangle is a right triangle (has 90 degree angle). Recall that in the right triangle, A^2 +B^2 = C^2
i'm really confused on this one.

Answer 1

y = 2.5x + 8
this is the slope-intercept form, so
slope = 2.5
y-intercept = 8
you got those right

The x-intercept is where y=0, so
2.5x+8 = 0
2.5x = -8
x = -16/5 = -3.2

The Pythagorean Theorem states that in a right triangle with sides a and b and hypotenuse c,

a^2+b^2 = c^2

So, to see whether your triangle is a right triangle, you need

6^2+8^2 = 12^2
36+64 = 144
100 = 144
Bzzzt! So it is not a right triangle.

Just FYI, the most basic right triangle has sides 3,4,5
If you scale up by a factor of 2, that gives sides of 6,8,10
So, 6,8,12 cannot be a right triangle.

Answer 2

Thank you!