Answer:
y=x+3
Step-by-step explanation:
perpendicular lines have slopes that are negative and reciprocal. If you multiply them together, the result is -1.
here is the equation: y=-x+4
the slope is -1
here is the equation to find the slope of the perpendicular line:
-1m=-1
multiply by -1
m=1
here is the new line so far: y=1x+b
now, we can substitute the point (2,5) into the equation, since the equation will pass through that point to find b (the y intercept)
5=1(2)+b
5=2+b
3=b
the equation of the line is y=1x+3, or y=x+3
Hope this helps!
Answer:
C(7.2,0.7)
Step-by-step explanation:
Let point C be
of the way from A to B, then ![AC:CB=7:3.](https://tex.z-dn.net/?f=AC%3ACB%3D7%3A3.)
If point
divides segment AB with endpoints
in the ratio
then
![x_C=\dfrac{nx_A+mx_B}{m+n}\\ \\y_C=\dfrac{ny_A+my_B}{m+n}](https://tex.z-dn.net/?f=x_C%3D%5Cdfrac%7Bnx_A%2Bmx_B%7D%7Bm%2Bn%7D%5C%5C%20%5C%5Cy_C%3D%5Cdfrac%7Bny_A%2Bmy_B%7D%7Bm%2Bn%7D)
In your case, A(-4,-7) and B(12,4), so
![x_C=\dfrac{3\cdot (-4)+7\cdot 12}{7+3}=\dfrac{-12+84}{10}=7.2\\ \\y_C=\dfrac{3\cdot (-7)+7\cdot 4}{7+3}=\dfrac{-21+28}{10}=0.7](https://tex.z-dn.net/?f=x_C%3D%5Cdfrac%7B3%5Ccdot%20%28-4%29%2B7%5Ccdot%2012%7D%7B7%2B3%7D%3D%5Cdfrac%7B-12%2B84%7D%7B10%7D%3D7.2%5C%5C%20%5C%5Cy_C%3D%5Cdfrac%7B3%5Ccdot%20%28-7%29%2B7%5Ccdot%204%7D%7B7%2B3%7D%3D%5Cdfrac%7B-21%2B28%7D%7B10%7D%3D0.7)
For this case, the first thing we must do is define variables.
We have then:
x: number of years
y: total change in time (seconds)
We now write the equation that models the problem.
We know that each year the time decreases by 8 seconds.
Therefore, the equation is:
![y = 8x](https://tex.z-dn.net/?f=%20y%20%3D%208x%20%20)
For the year number 5 we have:
![y = 8 (5)\\y = 40](https://tex.z-dn.net/?f=%20y%20%3D%208%20%285%29%5C%5Cy%20%3D%2040%20%20)
Answer:
the total change in time is 40 seconds