Question

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Answer 1

Hey!


Alright, let's see here. To find the y-intercept of the equation, we simply must graph the equation and find out at what point does the line intercept with the y axis.

Below the answer I have provided a picture of your equation graphed. When looking at it you can see right away that the y-intercept is 0.5.

Now, the other part of your question asks us to solve what the slope is. There is two methods you could use to solve this. But I'll just use a method that is called standard form.

Standard from is $Ax + By = C$. $A$ is a positive integer, while $B, C$ are integers.

To use standard from to find the slope of the equation, we must first convert the equation to standard form. To do that, we'll first expand the equation.

Original Equation :
2 ( y + 1 ) = 10x + 3

New Equation {Changed by Expanding it} :
2y + 2 = 10x + 3

Now we'll subtract two from both sides to simplify it. This will help us get 2y on its own.

Old Equation :
2y + 2 = 10x + 3

New Equation {Simplified} :
2y = 10x + 1

Next, we'll subtract 10x from both sides to simplify it even further. This will get help us get rid of the 10x that is on the right side of the equation.

Old Equation :
2y = 10x + 1

New Equation {Simplified} :
-10x + 2y = 1

Once again, we are going to multiply both sides of the equation by -1.

Old Equation :
-10x + 2y = 1

New Equation {Simplified} :
10x - 2y = -1

Now that our equation matches standard form, we can now continue on finding the slope. It is important to remember that slope m of a line is of the standard form $Ax + By = C$ which equals $- \frac{A}{B}$.

Okay, so according to standard form in our equation A = 10 and B = -2. Let's plug that into our equation.

$- \frac{A}{B} = -\frac{10}{-2}$

Now we simply simplify and we get 5. So, the slope is 5.

So, this means that for the equation 2 ( y + 1 ) = 10x + 3 the  y-intercept is 0.5  and  the slope is 5.

Hope this helps!


- Lindsey Frazier ♥