Question

What is the slope of (y-14)=5(x-7)

Answer 1

5

Explanation:

We want to put the equation into the form y=mx+b, where m is the slope and b is the y-intercept (what the y is when x=0 also known as the point where the line hits the y-axis)

First we can distribute the 5 to the x-7 by multiplying it by both terms. We get:

`(y-14)=5x-35`

The parentheses around the y-14 don't do anything, so we can get rid of them. The equation is:

`y-14=5x-35`

We can add 14 to both sides

`y-14+14=5x-35+14`

`y=5x-21`

If we compare this to the equation y=mx+b. We see that the 5 is in the spot of the m and the -21 is in the spot of the b.

This means that m=5 and b=-21. Putting in our definitions, the slope is 5 and the y-intercept is -21.

Because we are looking for the slope, the answer is 5.

Answer 2

Slope

We are given an equation in point-slope form, which is:

• 
  `\bf{y-y_1=m(x-x_1)}`

Where m is our slope.

Now let's look at our equation:

`\bf{y-4=5(x-7)}`

We know that:

`\bf{y-14=\overbrace{5}^(slope)(x-7)}`

Therefore, the line's slope is 5. Look at the number in front of the parentheses - it will tell you the slope.