Question

Write the following in slope-intercept form.

Answer 1

`\huge\boxed{y=4x-7}`

Explanation:

Linear equations will always be in the form
`y=mx+b`, where m is the slope and b is the y-intercept

Since we know nothing about this equation, other than the fact that there are two points in it, we must find the slope and the y-intercept.

Luckily, we have two points to work with. We know that the slope between two points will be the change in y divided by the change in x (
`(\Delta y)/(\Delta x)`), so we can use the two points given to us to find both changes.

The y value goes from 1 to 17, which is a
`17-1=16` change.

The x value goes from 2 to 6, which is a
`6-2=4` change.

Now that we know both changes, we can divide the change in y by the change in x.

`(16)/(4)=4`

Now that we know the slope (4), we can plug it into our equation (
`y=mx+b`).

`y=4x+b`

Now all we need to do is find the y-intercept. Since we know the slope and one of the points the line passes through, we can find the y-intercept by substituting in the values of x and y. Let's use the point (2, 1).

• 
  `1 = 4(2) + b`

• 
  `1 = 8+b`

• 
  `b = 1-8`

• 
  `b = -7`

Therefore our y-intercept is -7. Now that we know the slope and the y-intercept, we can plug it into our equation.

`y=4x-7`

Hope this helped!