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What is the y-coordinate of the point in the standard (x,y) coordinate plane at which the 2 lines y = x/2 + 3 and y = 3x − 2 intersect?
- a)5
- b)4
- c)3
- d)2
- e)1
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
What is the y-coordinate of the point in the standard (x,y) coordinate...
The correct answer is b. To find the y-coordinate where the 2 lines y = x/2 + 3 and y = 3x −2 intersect, you could set x/2 + 3 equal to 3x − 2 because they are both already solved for y. Where they would intersect, their y-coordinates would be equal. To solve x/2 + 3 = 3x − 2, you could add 2 and subtract x/2 to both sides to get 5x/2 = 5, then multiply by 2/5 (the reciprocal of 5/2) to get x = 2. Then simply substitute 2 for x into either of the initial equations to get y = 4.
Community Answer
What is the y-coordinate of the point in the standard (x,y) coordinate...
To find the y-coordinate of the point where the two lines intersect, we need to set the equations equal to each other and solve for y.
Setting y = x/2 + 3 equal to y = 3x, we get:
x/2 + 3 = 3x
Multiplying both sides of the equation by 2 to eliminate the fraction, we get:
x + 6 = 6x
Subtracting x from both sides, we get:
6 = 5x
Dividing both sides by 5, we get:
x = 6/5
Now, substituting this value of x into either of the original equations, we can find the corresponding y-coordinate.
Using y = x/2 + 3:
y = (6/5)/2 + 3
y = 3/5 + 15/5
y = 18/5
Therefore, the y-coordinate of the point where the two lines intersect is 18/5.
Setting y = x/2 + 3 equal to y = 3x, we get:
x/2 + 3 = 3x
Multiplying both sides of the equation by 2 to eliminate the fraction, we get:
x + 6 = 6x
Subtracting x from both sides, we get:
6 = 5x
Dividing both sides by 5, we get:
x = 6/5
Now, substituting this value of x into either of the original equations, we can find the corresponding y-coordinate.
Using y = x/2 + 3:
y = (6/5)/2 + 3
y = 3/5 + 15/5
y = 18/5
Therefore, the y-coordinate of the point where the two lines intersect is 18/5.
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