Answer:
Use the equation y = -1/2x + 2, answer is in attached image.
Explanation:
Arrange into y - intercept form which is:
y = mx + b
Where "y" is the dependent variable and "x" is the independent variable. "m" represents the slope and "b" represents the y - intercept, which is the intersection of the equation of this line and the y - axis.
Once we rearrange this equation into this format, we can then graph the line using the slope("m") and the y - intercept ("b"), (note: if the y - intercept of an equation is 0 or not there, then the line starts from the origin, which is (0, 0).
We are given:
4x + 8y = 16
Now to get this into y = mx + b, we have to get "y" alone.
Subtract 4x from both sides as we are using the inverse operation of addition which is subtraction:
-4x -4x
8y = -4x + 16
Now, divide both sides by 8 as we only want "y" alone since the inverse operation of multiplication is division:
/8 /8
y = -4/8x + 16/8
Simplify:
y = -1/2x + 2
Our equation is y = -1/2x + 2.
So now we have to find the slope and y - intercept:
The "m" is the slope, and in this case the slope is -1/2.
The "b" is the y - intercept, and in this case the y - intercept is 2.
Now, the first step into graphing an equation is to plot the y - intercept, the y intercept is 2, so our point is (0, 2).
Plot (0, 2).
Now the next step is to follow the slope. What I mean by "follow", you have to plot different points according to the slope (rise/run).
The slope is -1/2, so the rise is -1 and the run is 2.
-1 essentially means you are going down one unit and 2 means that you are going 2 units to the right.
So, plot points that start from 2(our y - intercept) and go down one over 2.
Once you have this, you'll get one side of the line, but we can extend it more to the other side. In order to do this, you have to find the opposite signs of our rise and run and go by that.
So in this case our slope is -1/2, the opposite of our rise (-1) is 1 since the opposite symbol of a negative is positive. Let's apply the same thing to our run too: the opposite of our run (2) is -2 since the opposite symbol of a positive number is a negative sign. Our slope to extend the line to the other side is 1/-2, REMEMBER: this does not change our original slope.
Now we apply this and start from our y - intercept again and rise/go up one unit and go to the left 2 units. Then consistently plot enough points so you can draw a line through all points using a straight edge (can be a ruler).
You'll be left with a graph that looks like the one I have attached below: