Question

Write the following in slope-intercept form.

Answer 1

Answer:

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

Step-by-step 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 ($\frac{\Delta y}{\Delta x}$), 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.

$\frac{16}{4}=4$

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!