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The expression y=-3x+6 and y=2x-4 represent straight lines: True/ False Compute the coordinates of the point at which the intersect: True/ False

User Hexwab
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Final answer:

The expression y=-3x+6 and y=2x-4 represent straight lines, and this is true. The point of intersection can be found by setting the two equations equal to each other and solving for x and y; the intersecting point is at coordinates (2, 0).

Step-by-step explanation:

The statements y=-3x+6 and y=2x-4 do indeed represent straight lines. This is true because they are both in the form of y=mx+b, where m is the slope and b is the y-intercept. According to Figure A1, the slope of a line is the ratio of the rise over the run, and the y-intercept is where the line crosses the y-axis.

To compute the coordinates of the point at which these lines intersect, we can set the two equations equal to each other since they both equal y:

  • -3x + 6 = 2x - 4

Adding 3x to both sides gives us:

  • 6 = 5x - 4

Adding 4 to both sides results in:

  • 10 = 5x

Dividing both sides by 5 gives us:

  • x = 2

To find y, we substitute x back into one of the original equations:

  • y = 2(2) - 4
  • y = 4 - 4
  • y = 0

So, the intersecting point of the two lines is at coordinates (2, 0).

User Lovetomato
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