Compare the y-intercepts and rates of change of the following items. 1) y=1.2x+0.4 2)a line which passes through the points (3,4) and (8,10)
A) how to change are the same, but the Y intercepts are different
B) the items that have different Y intercepts in different rates of change
C) the Y intercepts are the same, but the rates of change are different
D) the items have the same way intercepts, and the same rate of change
That’s wrong
Apologies for the mistake. Let's reassess the options and compare the given items.
1) The equation y=1.2x+0.4 represents a line with a y-intercept of 0.4 and a rate of change (slope) of 1.2.
2) In order to find the equation of the line passing through the points (3,4) and (8,10), we must first calculate the slope. The slope (rate of change) is found by taking the difference in y-coordinates divided by the difference in x-coordinates: (10-4)/(8-3) = 6/5 = 1.2. The y-intercept can be found by substituting one of the points into the slope-intercept form equation, y = mx + b, and solving for b. Using point (3,4), we have: 4 = 1.2(3) + b. Solving for b, we find b = -0.4. Therefore, the equation of the line passing through the points (3,4) and (8,10) is y = 1.2x - 0.4.
Comparing the y-intercepts, we can see that they are different (0.4 vs -0.4). However, the rates of change are the same (1.2).
Therefore, the correct answer is:
A) The y-intercepts are different, but the rates of change are the same.
C) the Y intercepts are the same, but the rates of change are different
Explanation:
1) The equation y=1.2x+0.4 represents a line with a y-intercept of 0.4 and a rate of change (slope) of 1.2.
2) The line passing through the points (3,4) and (8,10) can be represented by the equation y=1x-1. The y-intercept is -1, and the rate of change (slope) is 1.
Therefore, the y-intercepts are different (0.4 vs -1), and the rates of change are different (1.2 vs 1).