Final answer:
The slope of the line through (3, 4) and (8, -3) is calculated by the difference in y-values divided by the difference in x-values, yielding -7/5 or -1.4, which does not match any of the provided options. Slope measures the steepness of a line and is consistent for any two points on a straight line.
Step-by-step explanation:
The slope of a line passing through two points, (3, 4) and (8, -3), can be found using the formula for slope:
slope (m) = (change in y) / (change in x) = (y2 - y1) / (x2 - x1). Plugging in our values, we get:
m = (-3 - 4) / (8 - 3) = -7 / 5 = -1.4. So, the correct answer would be none of the options provided (A) -1, (B) 1, (C) -2, (D) 2, indicating a possible typo in the question or the options provided.
The slope is a measure of how steep a line is. In FIGURE A1 Slope and the Algebra of Straight Lines, the slope of 3 means for every increase of 1 on the horizontal axis, there is a rise of 3 on the vertical axis. The value of the slope (m) and y-intercept (b) in the equation of a straight line (
y = mx + b) determine the shape of the line.