Question

a. $y = - 5x+4$ b. $y =-\frac{1}{5}x + 4$ c. $y=\frac{1}{5}x - 4$ d. $y = 4x+5$ 8. graph the right triangle with the points (6,1) and (3,5) forming the hypotenuse. using the sides find the distance between the two points. leg :______ leg: ____ hypotenuse: ______

Explanation:

Step1: Identify the distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $(x_1,y_1)=(3,5)$ and $(x_2,y_2)=(6,1)$.

Step2: Calculate the differences in x - and y - coordinates

$x_2 - x_1=6 - 3=3$ and $y_2 - y_1=1 - 5=- 4$.

Step3: Square the differences

$(x_2 - x_1)^2=3^2 = 9$ and $(y_2 - y_1)^2=(-4)^2 = 16$.

Step4: Sum the squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=9 + 16=25$.

Step5: Take the square - root

$d=\sqrt{25}=5$.

For the legs of the right - triangle:
The horizontal leg length is the absolute value of the difference in x - coordinates. The difference in x - coordinates is $6 - 3 = 3$, so the length of one leg is 3.
The vertical leg length is the absolute value of the difference in y - coordinates. The difference in y - coordinates is $1 - 5=-4$, and its absolute value is 4.

Answer:

Leg: 3
Leg: 4
Hypotenuse: 5