O Matt 6.RPA3
2 answers:
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Answer:
Step-by-step explanation:
We are given that a line has a slope of -2/3 and passes through the point (0,6)
We want to write the equation of this line; there are 3 forms of the line that we can use:
- Slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept
- Standard form, which is ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be 0, and a cannot be negative
- Slope-point form, which is
, where m is the slope and
is a point
All though while writing the equation of the line in any of these ways is acceptable, the most common way is to write it in slope-intercept form, so let's do it that way.
As we are already given the slope, we can immediately substitute m with that value.
Replace m with -2/3:
y = -2/3x + b
Now we need to find b.
As the equation passes through the point (0, 6), we can use it to help solve for b.
Substitute 0 as x and 6 as y.
6 = -2/3(0) + b
Multiply
6 = 0 + b
Add
6 = b
Substitute 6 as b.
y = -2/3x + 6
Topic: finding the equation of the line
See more: brainly.com/question/27645158
Answer:
see the procedure
Step-by-step explanation:
Let
x ----> the number of dogs
y ---> the number of cats
we know that
The ratio of the number of dogs to the number of cats is 4:5
so
----> equation A
That means ---> The number of dogs is 4/5 the number of cats
There are 270 animals on the rescue farm
so
----> equation B
Substitute equation A in equation B
solve for y
Find the value of x
<u><em>Verify each statement</em></u>
a) The number of dogs is 4/5 the number of cats
The statement is true (see the explanation)
b) 4/5 of the pets at the farm are dogs
The statement is false
Because
(4/5)(270)=216 dogs
The number of dogs is 120 not 216 (see the explanation)
c) There are exactly 30 more cats than dogs
The statement is true
Because, there are 150 cats and 120 dogs (see the explanation)
d) There are exactly 30 dogs at the farm
The statement is false
Because, there are 120 dogs in the farm (see the explanation)
e) 5/9 of the pets at the farm are cats
The statement is true
Because
(5/9)270=150 cats
The number of cats is 150 (see the explanation)