Can someone please help me with#6-#8?I'm not sure how to find the answers and graph it in the graphs given.
1 answer:
Answers:
- 6. Slope = -5/3; y intercept = 5
- 7. Slope = -1; y intercept = 2
- 8. Slope = 3; y intercept = 0
The graphs are below
========================================================
Explanation:
6)
Let's solve for y to get the equation in slope intercept form y = mx+b
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.
---------------------------------
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.
---------------------------------
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.
You might be interested in
Answer:
Step-by-step explanation:
This is an exponential equation that is solved by taking the natural log of both sides. The equation is
If we are looking for x when f(x) = 64, then
Take the natural log of both sides:
The rules of logs allows us to bring the x down in front:
Divide both sides by ln(2) to get:
Do this on your calculator to get that x = 6.
You could also have just gone right to your calculator and started raising 2 to consecutive powers starting at like 3 or 4 to eventually get that 2 to the 6th power is equal to 64, but for the basics of solving log equations, you need to know how to do this.
Answer:
x = -1
Step-by-step explanation:
When an exponent is negative, you have to move it to the denominator (or to the numerator if it's already on the denominator). Since the answer is , you know that the 2 has been raised to the power of 1 (any number to the power of 1 is the same number), so you just make it negative. Hope that helps!