write the equation of the line that passes through (1, 5) and (−2, 14) in the slope-intercept form.

a- y = 3x + 2
b- y = 3x + 8
c-y = −3x − 2
d- y = −3x + 8

d

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (1, 5) and (x₂, y₂ ) = (- 2, 14)

m = = = - 3, thus

y = - 3x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (1, 5), then

5 = - 3 + c ⇒ c = 5 + 3 = 8

y = - 3x + 8 → d

a) justify

step-by-step explanation:

justifying is just part of everyday life. justify kind of means proof so i think the answer is a) justify.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47