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:
Adding 3x to both sides gives us:
Adding 4 to both sides results in:
Dividing both sides by 5 gives us:
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).