Answer:
Look below :)
Step-by-step explanation:
1. To find the slope of a line, we can use this expression:
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:
=
Let's solve for the slope:
20 - 4 = 16
12 - 4 = 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!