Question

DUE SOON PLS HELP: All of the points on the picture are on the same line. 1. Find the slope of the line. Explain your reasoning.

Answer 1

Answer:

Look below :)

Step-by-step explanation:

1. To find the slope of a line, we can use this expression: $\frac{y2 - y1}{x2 - x1}$

In order to use that expression, we need to use two points. The graph given only provides you with two complete points, so we'll use those.

(4, 4) = (x1, y1)  (12, 20) = (x2, y2)

Now we can input the values into the expression:

$\frac{y2 - y1}{x2 - x1}$ = $\frac{20 - 4}{12 - 4}$

Let's solve for the slope:

20 - 4 = 16

12 - 4 = 8

$\frac{16}{8}$

To simplify 16/8 divide both the numerator and the denominator by 8:

16/8 = 2

8 = 1

You get 2/1 or just 2.

The slope of the line is 2.

2. To make an equation for the line, we'll use slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. We already know the value of the slope is 2, so now we need to find the y-intercept. We can find the y-intercept using a given point and the slope. In this example, I'll use the point (4, 4). Let's input the values into the equation:

y = mx + b

4 = 2(4) + b

Now let's solve for b:

4 = 8 + b

Subtract 8 from both sides to isolate the b:

4 - 8 = 8 - 8 + b

-4 = b

The y-intercept of the equation is -4.

Now that we know the values for the slope and y-intercept, we can write the equation:

y = 2x - 4

3. To find the values of a and b, we can use the equation we made in the previous question.

First we'll find a:

The point we are given is (a, 16). We know the y-value is 16, so we can put that into our equation. We can also replace x with a:

y = 2x - 4

16 = 2a - 4

Now we can solve for a:

First, add 4 to both sides to isolate the 2a:

16 + 4 = 2a - 4 + 4

20 = 2a

Then divide both sides by 2 to isolate a:

20/2 = 2a/2

10 = a

The value of a is 10.

Now let's find b:

This is similar to finding a. The point we are given is (8, b). We know the value of x is 8, and we can replace y with b in the equation:

y = 2x - 4

b = 2(8) - 4

Let's solve:

b = 2(8) - 4

b = 16 - 4

b = 12

The value of b is 12.

4. Finally, to find the y- coordinate when x=0, all we have to do is input 0 in for x in the equation and then solve for y:

y = 2x - 4

y = 2(0) - 4

y = 0 - 4

y = -4

When x = 0, y = -4.

The answer for what the y-coordinate is when x = 0 will always be the value of the y-intercept.

I hope this helps!

Answer 2

I did all of my work on a piece of paper.