(15 POINTS!) The slope of the line passing through the points (7, 5) and (21, 15) is

5/7
7/5
5
7

Another line with a slope that is one-third that of the slope you just calculated passes through the origin and the point

3, 5
3, 7
21, 5
21, 7

1) 5/7

2) (21, 5)

Step-by-step explanation:

1) The slope of the line passing through the points (7, 5) and (21, 15) is

because slope is (difference of y)/(difference of x)

the first option is correct

2) 1/3 of 5/7 is 5/21.

The line will be in the form of

y = 5/21 x + b where b is the y-intercept.

Find the complete equation by plugging in (0,0) since it passes thorugh the origin.

0 = 5/21 (0) +b

0=0+b

b=0

The equation: y=5/21 x

let's check each option by plugging in.

y= 5/21 (3)= 5/7

y is not 5 but 5/7

y= 5/21 (3)= 5/7

y is not 7 but 5/7

y= 5/21 (21) = 5

y is 5, which matches with the answer choice!!!

y= 5/21 (21) = 5

y is 5, not 7.

The third option is correct

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus

proportions are fractions that equal to each other. so if two fractions are the same, they are proportional.

let's check the answers to see if they are proportional.

question a is not proportional because you can't turn 1.5/3 to 3/9. if you try to multiply 1.5/3 by 2 or 3, you wont get 3/9. it's impossible to make the fractions the same.

question b is not proportional because you can't turn 22/33 to 4/6. 33 can't go into 6.

question c is proportional because when you multiply 2 and 3 by 71, you would get 142/213, and those fractions equal to each other

question d is proportional because when you divide 14 and 7 by 2, you would end up with 7/3.5, and those fractions equal to each other.