Answer: A straight line through (0,-9) and (3,-4)
The graph is shown below.
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Step-by-step explanation
I'll show two methods.
Method 1
is the same as y = (5/3)x - 9 when writing it out on a computer keyboard.
The equation y = (5/3)x - 9 is of the form y = mx+b
- m = 5/3 = slope
- b = -9 = y intercept
The y intercept is our anchor point. Always start here. It represents the location (0,-9).
From that anchor, move 5 units up and 3 units right. This "up 5, right 3" motion is directly from the slope 5/3. Recall that slope = rise/run.
Start at (0,-9) and follow the "up 5, right 3" pathway to arrive at (3,-4)
Then plot the two points (0,-9) and (3,-4). The last step is to draw a straight line through them. See the graph below. GeoGebra was used to make the graph. Desmos is another option.
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Method 2
To plot a line, we need 2 points on it. Each point is of the format (x,y)
Select random values for x to find their corresponding y coordinates.
For instance, if x = 0, then,
y = (5/3)x - 9
y = (5/3)*0 - 9
y = 0 - 9
y = -9
The input x = 0 leads to the output y = -9
We have the point (0,-9) that was mentioned in the previous section. It's the y intercept.
Repeat the process with another x value. You could pick x = 1, but it leads to messy fractions.
It's better to pick x = 3 since it cancels with the denominator.
If x = 3, then,
y = (5/3)x - 9
y = (5/3)*3 - 9
y = 5 - 9
y = -4
We arrive at (3,-4) that was mentioned in the previous section.
And also mentioned previously is that we plot the two points and then draw a straight line through them.
See the graph below.