Question

give reasons for your slopes at each point are independent of y, so the slopes are the same along each line parallel to the y-axis. note that for y

Answer 1

The slope of a straight-line graph is the same along the entire line and is independent of the y-coordinate because it is defined as the ratio of the change in y to the change in x, which is constant for a straight line.

Step-by-step explanation:

The question deals with the concept of slopes in a straight-line graph. When two variables are plotted on a graph with perpendicular axes, the slope of a straight line is constant along the line and is independent of the y-coordinate. This is because the slope of a straight line is defined by the change in y divided by the change in x (rise over run), which remains the same regardless of where you are on the line.

For example, in Figure A1, the slope is shown to be 3, meaning for every unit you move along the x-axis, the line rises by 3 units on the y-axis. This ratio stays the same along the entire length of the line, hence the slope is the same for any point on that line.

The y-intercept, represented by the variable b in the equation y = mx + b, simply tells us where the line crosses the y-axis, but it does not affect the slope of the line.