(05.02) A line passes through (2,8) and (3, 12).
1. What is the slope of this line?
2. What is the y-intercept (show/explain how you know)
3. What is the equation of this line?

1. the slope is 4

2. the y intercept is 0

3. the equation of the line is y=4x

Step-by-step explanation:

First let's find the slope of the line (m)

Let's use the formula (y2-y1)/(x2-x1)

here are the points: (2,8) and (3,12)

let's label them

x1=2

y1=8

x2=3

y2=12

now substitute into the equation.

m=(12-8)/(3-2)

m=4/1

m=4

The slope of the line is 4.

Now, to find the y intercept:

You might have noticed that to go from (2,8) to (3,12), you add 1 to x and 4 to y.

Therefore, to find the y intercept, where the line crosses the y axis, you can first subtract 1 from x and 4 to y to get another point that fits on the line (1,4) and then again to get the point: (0,0)

therefore, the y intercept is 0

the most common method of the equation of the line is y=mx+b, where m is the slope and b is the y intercept

therefore the equation of the line is y=4x+0 or y=4x

Hope this helps!

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)