Answer:
Explanation:
The rate of change of y with respect to x for a line is represented by the slope of the line. The slope is usually denoted by the letter "m."
In this case, the options given are:
1. 2/5
2. 1
3. -2/
4. -1
To determine the rate of change of y with respect to x, we need to find the slope of the line.
The slope of a line is calculated by taking the difference in y-coordinates (vertical change) and dividing it by the difference in x-coordinates (horizontal change) between two points on the line.
If we are given the equation of the line, we can determine the slope by looking at the coefficient of x. For example, if the equation of the line is y = mx + b, where m is the slope, then the rate of change of y with respect to x is equal to m.
However, since we are only given options and not the equation of the line, we need to identify the correct option that represents the slope.
Let's analyze each option:
1. 2/5: This option represents a slope of 2/5, which means that for every 5 units of horizontal change (x), there will be a corresponding vertical change (y) of 2 units. Therefore, the rate of change of y with respect to x for this line is 2/5.
2. 1: This option represents a slope of 1, which means that for every 1 unit of horizontal change (x), there will be a corresponding vertical change (y) of 1 unit. Therefore, the rate of change of y with respect to x for this line is 1.
3. -2/: This option seems to have a typo or is incomplete. It does not provide a valid value for the slope.
4. -1: This option represents a slope of -1, which means that for every 1 unit of horizontal change (x), there will be a corresponding vertical change (y) of -1 unit. Therefore, the rate of change of y with respect to x for this line is -1.
Based on the analysis, the correct options for the rate of change of y with respect to x for this line are 2/5 and -1, as represented by options 1 and 4, respectively.