The slope-intercept form of the equation of a line that passes through point (-3, 8) is y=-2/3x+6. What is the point-slope form
of the
equation for this line?
equation for this line?
1 answer:
Answer:
b. y - 8 = -2/3(x + 3)
Step-by-step explanation:
Well point-slope form takes one point in this case (-3,8) and puts it into the equation.
So this is point slope form,
The 2 negatives in the -y and -x means you have to change the number to a negative to a positive to a negative.
We plug in (-3,8) to the equation.
y - 8 = m(x + 3)
Well we change the -3 to a 3 because of the negative.
So with the given slope -2/3 we plug that in for m.
y - 8 = -2/3(x + 3)
<em>Thus,</em>
<em>answer choice b is correct.</em>
<em />
<em>Hope this helps :)</em>
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Answer:
Fred C. 16.30 ft
Gary B. 169.67 m
Step-by-step explanation:
Fred the owl...
Always <u>draw a diagram first</u> (see diagram below). We assume trees are perpendicular (at 90°) to the ground. The situation forms a right-angle triangle.
We need to <u>find "x"</u>, which is the direct distance between the owl and the bird. "x" is also the hypotenuse, which is the longest side in a right-angle triangle. Since we know a side and an angle, we can find the hypotenuse using primary trigonometry ratios.
∠B will be the angle of reference (the angle we are "talking" about). The side we know is opposite to ∠B (15ft). We know it's opposite because it's not touching the angle. The side we need to find is the hypotenuse.
<u>Use the trig. ratio sine</u> because it has opposite and hypotenuse in it. The general formula is:
sinθ = opp/hyp
θ means the angle, and we know it is 67°.
Replace all the information you know:
sinB = opp/hyp
sin67° = (15ft) / x Isolate "x". Rearrange the equation.
xsin67° = (15ft) Divide both sides by sin67°
x = (15ft) / sin67°
x = 16.295... ft Exact answer in decimals
x ≈ 16.30 ft Rounded to nearest hundredth
Therefore Fred the owl is 16.30 feet from the bird.
Gary spots a monkey...
Draw a diagram first (see below). G is Gary, M is the monkey, T is the bottom of the Sears Tower. We need to <u>find "x"</u>, which is the distance between the monkey and the bottom of the tower.
The angle of reference is M, which is 69°. We need to find the adjacent side and we know the opposite side. <u>The trig. ratio that has adjacent and opposite is tangent.</u>
tanθ = opp/adj
Replace all the information you know:
tanM = opp/adj
tan69° = (442m) / x Rearrange the formula to isolate "x"
xtan69° = 442m Divide both sides by tan69°
x = 442m / tan69° Solve by dividing
x = 169.6679.... m Exact decimal answer
x ≈ 169.67m Rounded to the nearest hundredth
Therefore the monkey is 169.67 metres from the tower.
Remember all the trig. ratios using the acronym SohCahToa.
o = opposite side
a = adjacent side
h = hypotenuse side
S = sine, sin for short
C = cosine, cos for short
T = tangent, tan for short
The operation is always dividing the first side in the acronym by the second side.
sinθ = opp/hyp
cosθ = adj/hyp
tanθ = opp/adj
