Mathematics, 30.08.2019 22:50 gulleraliyeva1999

What is the equation of the line that is parallel to the given line and has an x-intercept of –3?
a) y = 2/3x + 3
b) y = 2/3x + 2
c) y = -3/2x + 3
d) y = -3/2x + 2

What is the equation of the line that is parallel to the given line and has an x-intercept of –3?

Answers: 2

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Answer from: dylancasebere

First, we must find the equation of the given line. The slope is "rise over run," or the change in y over the change in x from one point to another.
The two points shown are (0,-1) and (3,1). In these points, y increases by 2. This means the change in y is 2. In these points, x increase by 3. This means the change in x is 3. Thus, the change in y over change in x is 2/3. This means that the slop of the given line is 2/3.

In the form y=mx+b, where m is the slope, b is the y intercept. This is because the y intercept occurs when x is 0. If x is zero, mx is zero, so y=b. In other words, when x equals 0, y=b. This creates the point (0,b), which is the y-intercept. Since the y-intercept of the given line is -3, the equation for this line is: y=2/3x-3.

A line parallel to this will need to have the same slope. This allows us to eliminate choices C and D, which do not have the same slope.

In order for the line to have an x-intercept of (-3,0), y must equal 0 when x is -3, since ordered pairs are (x,y). We can solve the equation using the information we know:
0=((2/3)(-3))+b
This is because we know the slope is 2/3, and that when x is -3, y is 0.

Then, we can solve from there:
0=(-2)+b (just multiply 2/3 and -3)
2=b (add 2 to both sides)

Thus, the correct equation is:
B) y=2/3x+2

Answer from: skullglitches

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Step-by-step explanation:

Answer from: Quest

7. 153.86 ft $^{2}$

8. 12.56 ft $^{2}$

9. 78.5 m $^{2}$

10. 379.94 in $^{2}$

11. 132.665 m $^{2}$

12. 12.56 yd $^{2}$

13. 226.865 ft $^{2}$

14. 113.04 ft $^{2}$

15. 63.585 ft $^{2}$

16. 254.34 m $^{2}$

17. 50.24 cm $^{2}$

step-by-step explanation:

7. $\pi x 7^{2} = \pi * 49 = 153.86 ft^{2}$

8. $\pi * 2^{2} = \pi * 4 = 12.56 ft^{2}$

9. $\pi * 5^{2} = \pi * 25 = 78.5 m^{2}$

10. $\pi * 11^{2} = \pi * 121 = 379.94 in^{2}$

11. $\pi * 6.5^{2} = \pi * 42.25 = 132.665 m^{2}$

12. $\pi * 2^{2} = \pi * 4 = 12.56 yd^{2}$

13. $\pi * 8.5^{2} = \pi * 72.25 = 226.865 ft^{2}$

14. $(\pi /4) * 12^{2} = 0.785 * 144 = 113.04 ft^{2}$

15. $(\pi /4) * 9^{2} = 0.785 * 81 = 63.585 ft^{2}$

16. $(\pi /4) * 18^{2} = 0.785 * 324 = 254.34 m^{2}$

17. $(\pi /4) * 8^{2} = 0.785 * 62 = 50.24 cm^{2}$

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Answer from: Quest

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What is the equation of the line that is parallel to the given line and has an x-intercept of –3?

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