Answer:
Step-by-step explanation:
The slope of a line characterizes the direction of a line. To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points .Teachers use different words for the y-coordinates and the the x-coordinates . Some call the y-coordinates the rise and the x-coordinates the run . Others prefer to use Δ notation and call the y-coordinates Δ , and the x-coordinates the Δ .These words all mean the same thing, which is that the y values are on the top of the formula (numerator) and the x values are on the bottom of the formula (denominator)!The slope of a line going through the point (1, 2) and the point (4, 3) is 13. Remember: difference in the y values goes in the numerator of formula, and the difference in the x values goes in denominator of the formula.Can either point be (1,1) ? There is only one way to know! First, we will use point (1, 2) as 1,1, and as you can see : the slope is: 13 . Now let's use point (4, 3) as 1,1, and as you can see , the slope simplifies to the same value: 13point (4, 3) as (1,1) =2−12−1=3−24−1=13 point (1, 2) as (1,1) =2−12−1=2−31−4=−1−3=13 Answer: It does not matter which point you put first. You can start with (4, 3) or with (1, 2) and, either way, you end with the exact same number! 1/3
Example 2 of the Slope of A line The slope of a line through the points (3, 4) and (5, 1) is −32 because every time that the line goes down by 3(the change in y or the rise) the line moves to the right (the run) by 2.This is because any vertical line has a Δ or "run" of zero. Whenever zero is the denominator of the fraction in this case of the fraction representing the slope of a line, the fraction is undefined. The picture below shows a vertical line (x = 1). vertical line The slope of a horizontal line is zero This is because any horizontal line has a Δ or "rise" of zero. Therefore, regardless of what the run is (provided its' not also zero!), the fraction representing slope has a zero in its numerator. Therefore, the slope must evaluate to zero. Below is a picture of a horizontal line -- you can see that it does not have any 'rise' to it.
