What is the volume of this prism? enter your answer as a mixed number in the simplest form.
2 answers:
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Answer:
Step-by-step explanation:
Hi there!
We want to find the equation of the line that passes through the point (-3, -6) and (2, -2)
There are 3 ways to write the equation of the line:
- In slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept
- In point-slope form, which is
, where m is the slope and
is a point
- In standard form, which is ax+by=c, where a, b, and c are integer coefficients, but a and b cannot be zero, and a cannot be negative
The easiest way would either be slope-intercept or point-slope form, but let's write the equation in slope-intercept form, since it's the most common way
So we'll need to find the slope
The formula for the slope calculated from 2 points is , where
and
are points
We have everything needed to find the slope, let's just label the values of the points to avoid any confusion:
Now substitute these values into the formula. Remember that m is the value of the slope:
m=
m=
Simplify the fraction:
m=
Add the numbers together:
m=
So the slope of the line is 4/5
Let's plug it into the formula y=mx+b, since we now know the value of m
y=x+b
Now let's find b
As the equation passes through both (-3, -6) and (2, -2), we can use either point to help solve for b
Either point works, but let's take (2, -2) for instance
Substitute 2 as x and -2 as y
-2=4/5(2)+b
Multiply
-2=8/5+b
subtract 8/5 from both sides
-18/5=b
Now substitute -18/5 as b into the equation:
Hope this helps!