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Mfcarla
20.02.2021 •
Mathematics
Unit: Exponents. radicals and scientific notation
Variable expressions with exponents
What is the value of x2 + y when = 3 and y = 4?
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What is the value of x^3+y^3 when x=3and y=4
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Ответ:
y = -1 x + 2
Step-by-step explanation:
First of all, remember what the equation of a line is:
y = mx+b
m is the slope, and b is the y-intercept.
Now, to find m, simply substitue here:![m=\frac{y1-y2}{x1-x2}](/tpl/images/1341/2418/25deb.png)
Which means: m =![\frac{-5-1}{7-1} = -1](/tpl/images/1341/2418/a0833.png)
Now, look at our line's equation so far: y=-1x+b.
b is what we want, the -1 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (1,1) and (7,-5).
So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!
You can use either (x,y) point you want..the answer will be the same:
Either: (1,1). y=mx+b or 1=-1 × 1+b, or solving for b: b=1-(-1)(1). b=2.
Or: (7,-5). y=mx+b or -5=-1 × 7+b, or solving for b: b=-5-(-1)(7). b=2.
both gave us the same answer for b, which is 2.
Therefore, the equation of the line that passes through the points (1,1), and (7,-5) is:
Y = -x + 2