Find the values of x and y that make these triangles congruent by the hl theorem

Option C x=2, y=6

Step-by-step explanation:

we know that

The hypotenuse leg theorem, (HL theorem), states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent

so

In this problem

Equate the hypotenuses of both right triangles

x+3=y-1 > x=y-4 > equation A

Equate the legs of both right triangles

y-3=2x-1 > equation B

substitute equation A in equation B and solve for y

y-3=2(y-4)-1

y-3=2y-8-1

2y-y=-3+9

y=6

Find the value of x

x=y-4 > x=6-4=2

therefore

x=2, y=6

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)

-2/