step 1
find the slope AB
A = (-3, -1) and B = (4, 4)
m=(y2-y1)/(x2-x1)------> m=(4+1)/(4+3)------> m=5/7
step 2
find the slope mBC
we know that
if two lines are perpendicular
then
the product of their slopes is equal to -1
so
mAB*mBC=-1-------> mBC=-1/mAB-----> -1/(5/7)-----> mBC=-7/5
step 3
with mBC and the point B = (4, 4) find the equation of the line BC
y-y1=m*(x-x1)-----> y-4=(-7/5)*(x-4)-----> y=-(7/5)*x+(28/5)+4---> y=-(7/5)*x+(48/5)
y=-1.4*x+9.6
therefore
the answer is
the equation of the line BC is
y=-1.4*x+9.6
see the attached figure
The decay factor of the equation given in the task content is; 0.87.
<h3>What is the decay factor from the equation?</h3>
According to the task content; the equation given is; y = 453(0.87)^4.
By comparison with exponential decay functions, it follows that the decay factor from the equation given is; 0.87 which insinuates that the factor of change after each decay is 0.87.
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You divide both sides by 14:
![14g>56 \iff \dfrac{14g}{14}>\dfrac{56}{14} \iff g>4](https://tex.z-dn.net/?f=14g%3E56%20%5Ciff%20%5Cdfrac%7B14g%7D%7B14%7D%3E%5Cdfrac%7B56%7D%7B14%7D%20%5Ciff%20g%3E4)
2 x 7, unless there’s options you have to choose from. 6-(-8)=14, so pretty much anything that equals to 14
Based on the calculations, the coordinates of the y-intercept are (0, -9).
<h3>What is the y-intercept?</h3>
In Mathematics, the y-intercept of any graph (parabola) occurs at the point where the value of "x" is equal to zero (0). Similarly, the x-intercept refers to the point at which the graph of a function crosses the x-axis and the value of "y" is equal to zero (0).
<h3>How to calculate the slope of a line?</h3>
Mathematically, the slope of any straight line can be calculated by using this formula;
![Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}](https://tex.z-dn.net/?f=Slope%2C%20m%20%3D%20%5Cfrac%7BChange%5C%3Bin%5C%3By%5C%3Baxis%7D%7BChange%5C%3Bin%5C%3Bx%5C%3Baxis%7D%5C%5C%5C%5CSlope%2C%20m%20%3D%20%5Cfrac%7By_2%5C%3B-%5C%3By_1%7D%7Bx_2%5C%3B-%5C%3Bx_1%7D)
Substituting the given parameters into the formula, we have;
Slope, m = (-4.5 - 3)/(-3 + 8)
Slope, m = -7.5/5
Slope, m = -1.5.
Mathematically, the standard form of the equation of a straight line is given by;
y - y₁ = m(x - x₁)
At point (-8, 3), we have:
y - 3 = -1.5(x + 8)
y - 3 = -1.5x - 12
y = -1.5x - 12 + 3
y = -1.5x - 9
Therefore, the coordinates of the y-intercept are (0, -9).
Read more on slope and y-intercept here: brainly.com/question/24787293
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