1) The points (-2,5) and (2,3) lie on the same line. Write the equation of the line in slope-intercept form. Type your answer in as y=mx+b. 2) The slope of a line is -12, and the line passes througin the point (0,8). Write the equation for the line in slope intercept form. Type your answer in as y=mx+b.
Answers
Answer:
1) The equation of the line is y = x + 4
2) The equation of the line is y = -12x + 8
Step-by-step explanation:
The slope-intercept form of the linear equation is y = m x + b, where
- m is the slope of the line, m = Δy/Δx (chang of y/change of x)
- b is the y-intercept (value y at x = 0)
Let us solve the two questions
1)
∵ points (-2, 5) and (2, 3) lie on the same line
→ Find the slope m
∵ Δ x = 2 - (-2) = 2 + 2 = 4
∵ Δ y = 3 - 5 = -2
∴ m =
∴ The slope of the line is
→ Substitute the value of m in the form of the equation above
∴ y = x + b
→ To find b substitute the x and y in the equation by the coordinates
of a point on the line
∵ Point (-2, 5) lies on the line
∴ x = -2 and y = 5
∵ 5 = (-2) + b
∴ 5 = 1 + b
- Subtract 1 from both sides
∴ 5 - 1 = 1 - 1 + b
∴ 4 = b
→ Sustitute it in the equation
∴ y = x + 4
The equation of the line is y = x + 4
2)
∵ The slope of the line is -12
∴ m = -12
∵ The line passes through point (0, 8)
∵ b is the value of y at x = 0
∴ b = 8
→ Substitute the values of m and b in the form of the equation above
∴ y = -12x + 8
The equation of the line is y = -12x + 8
Final answer:
The equations of the lines are y=-0.5x+4 and y=-12x+8 respectively. For the first line, the slope is computed using provided points and the y-intercept is calculated using one of the points and the slope. For the second line, we use provided slope and point to write the equation.
Explanation:
Firstly, let's deal with the first part of the question. To write the equation of the line, we first need to calculate the slope. The slope (m) is calculated as (y2-y1)/(x2-x1). Using the points (-2,5) and (2,3) we find m=(3-5)/(2-(-2))= -2/4 = -0.5. The y-intercept (b) is the y value when x = 0. To find b, let's use the point (-2,5) and the slope in the equation y=mx+b. We get 5=(-0.5)*-2+b, hence b= 5-1= 4. So line equation is y=-0.5x+4.
For the second part of the question, we know that the slope (-12) and it passes through the point (0,8). So the y-intercept is 8 when x=0. Therefore, the equation of this line is y=-12x+8.
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Write the equation for a parabola with the focus at(-1, 4) and the equation of the directrix x = 5.(x + 1)2 = 3(y-4)(y-4)2 = 12(x + 1)(y-2)2 = -3(x – 4)(y-4)2 = –12(x - 2)
2. Juan worked 2.5 hours and earned $37.00. Lisa was paid $42.00 for 3 hours of work. Which of the following statements is true?
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So " 60/100 " can be written "60%".
Answers
Tn=a₁r^(n-1)
In this case:
Tn=a₁r^n
Because:
T₁ corresponds to 0 minutes ⇒T₁=3000(1/2)⁰=3000
T₂ corresponds to 1 minute ⇒ T²=3000(1/2)¹=1500 ...
Tn=375
a₁=3000
r=1/2
n=number of minutes
Therefore:
375=3000*(1/2)^n
375/3000=(1/2)^n
0.125=(1/2)^n
Ln 0.125=ln [(1/2)^n]
Ln 0.125=n Ln(1/2)
Ln 0.125=n [Ln1-Ln2]
Ln 0.125=n[0-Ln 2]
n=Ln 0.125 / (-Ln2)
n=3
answer: 3 minutes.
b. 4
c. 9
d. 10
Answers
A) 2.
Explanation:
We know that |x|² = 13 and x = 3+bi:
(3+bi)² = 13
3² + b² = 13
9 + b² = 13
Subtract 9 from each side:
9 + b² - 9 = 13 - 9
b² = 4
Take the square root of each side:
√b² = √4
b = 2
A possible value of b is mathematically given as
b = 2
What is a possible value of b ?
Generally, the equation for the complex number is mathematically given as
x = 3 + bi and |x|^2 = 13,
Therefore
Take the square root of each side:
b = 2
In conclusion,
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A. 10a^4b^3
B. 3a^4b^4
C. 10a^4b^4
D. 3a^4b^3
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15a^9b^4 / 5a^5b = 3a^(9-5)b^(4-1) = 3a^4b^3
The correct result would be D. 3a^4b^3.
Answers