Answers:
- 6. Slope = -5/3; y intercept = 5
- 7. Slope = -1; y intercept = 2
- 8. Slope = 3; y intercept = 0
The graphs are below
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Explanation:
6)
Let's solve for y to get the equation in slope intercept form y = mx+b
[tex]5x+3y = 15\\\\3y = -5x+15\\\\y = \frac{-5x+15}{3}\\\\y = \frac{-5x}{3}+\frac{15}{3}\\\\y = -\frac{5}{3}x+5\\\\[/tex]
That last equation matches with y = mx+b to get
m = -5/3 = slope
b = 5 = y intercept
To graph this, we plot the y intercept at (0,5). Then move down 5 and to the right 3 to arrive at (3,0) as the second point. This movement is directly tied to the slope. We only need two points to graph a straight line.
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7)
The equation y = -x+2, aka y = -1x+2, is already in slope intercept form
m = -1 = slope
b = 2 = y intercept
Start at (0,2) which is the location of the y intercept. Move down 1 and to the right 1 due to the slope -1/1 = -1. This should move us to the point (1,1). Connect the two points (0,2) and (1,1) with a straight line to finish up the graph.
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8)
We start with the origin (0,0) because the y intercept of y = 3x is 0. It might help to think of y = 3x as y = 3x+0
Then we move up 3 units and to the right 1 unit to get to (1,3) as our next point. Connect the two points with a straight line
slope = 3
y intercept = 0
Once again, the graphs are shown below.
