A line intersects the x-axis at x = -4 and the y-axis al y = 3. Find the slope of the line

slope =

Step-by-step explanation:

Calculate the slope m using the slope formula

m =

with

(x₁, y₁ ) = (- 4, 0) and (x₂, y₂ ) = )0, 3) ← coordinates of intercepts

m = =

1) The problem says that the quilt squares are cut on the diagonal to form triangular quilt pieces. Then, the triangle pieces have angles of 45°, and the legs have the same lenght. So, you can solve the exercise by applying the Pythagorean Theorem:

 h²:s²+s²
 h²=2s²
 h²/2=s²
 s=√(h²/2)

 "h" is the hypotenuse (h=10 inches) and "s" is the length of the sides.

 When you substitute the value of the hypotenuse into the formula s=√(h²/2), you obtain the sides length:

 s=√(h²/2)
 s=√(10²/2)
 s=5√2

 What is the side length of each piece? 

 The answer is: 5√2

 2)Tan(α)=Opposite/Adjacent

 α=30°
 Opposite=17
 Adjacent=x

 When you substitute these values into Tan(α)=Opposite/Adjacent, you obtain:

 Tan(α)=Opposite/Adjacent
 Tan(30°)=17/x
 x=17/Tan(30°)
 x=17√3

 Sin(α)=Opposite/Hypotenuse

 α=30°
 Opposite=17
 Hypotenuse=y

 Then, you have:

 Sin(30°)=17/y
 ySin(30°)=17
 y=17/Sin(30°)
 y=34