Final answer:
Each of the given equations is in point-slope form, and they describe lines with specific points and slopes. The point and slope for the first equation are (4, 3) and 2 respectively, for the second are (8, -4) and -1/2, and for the third are (-1, 5) and -3.
Step-by-step explanation:
The equations given are in point-slope form, which is typically written as y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. To identify the point and the slope for each equation:
- For y - 3 = 2(x - 4), the point is (4, 3) and the slope is 2.
- For y + 4 = -1/2(x - 8), the point is (8, -4) and the slope is -1/2.
- For y - 5 = -3(x + 1), the point is (-1, 5) and the slope is -3.
The slope (m) represents the rate of change of the line, indicating how steep the line is, and it is consistent along the entirety of a straight line as shown in Figure A1. The point corresponds to where the line crosses the axes. This information illustrates the relationship between the linear equation and the geometric representation of the line on a graph.