The Slope of the given line is 5/2 and the equation of the line is y = 5/2 x - 4.
How do find the slope from the coordinate points of a line?
If a line is given with its coordinate points (x1, y1) and (x2, y2), then the slope can be found by the ratio of the difference of their y-coordinates to the difference of their x-coordinates. I.e., m = (y2 - y1)/(x2 - x1)
What is the equation of a line with two of its coordinate points?
The two coordinate points are (x1, y1) and (x2, y2)
Then the equation of the line is,
(y - y1) = [tex]\frac{(y2-y1)}{(x2-x1)}[/tex] × (x - x1)
Since we have [tex]\frac{(y2-y1)}{(x2-x1)}[/tex] = m (slope), we can write it as,
(y - y1) = m(x - x1)
This represents the point-slope form of a line.
Calculation:
Finding the slope from the given table:
The x coordinates are { 2, 4, 6, 8, 10, 12, 14} and the y coordinates are { 1, 6, 11, 16, 21, 26, 31}
So, consider any two coordinate points such as (2, 1) and (4, 6)
Then, x1 = 2, x2 = 4, y1 = 1, and y2 = 6
Slope = (y2 - y1)/(x2 - x1)
On substituting the values,
Slope = (6 - 1)/(4 - 2)
∴ m = 5 / 2
Finding the equation of the line:
Since we have the slope and a point (2, 1), we can use the point-slope form. I.e., (y - y1) = m(x - x1)
⇒ (y - 1) = 5/2 (x - 2)
⇒ 2y - 2 = 5x - 10
⇒ 2y = 5x - 10 + 2
⇒ y = 5/2x - 8/2
∴ y = 5/2 x - 4
Thus, the obtained equation is in the form of the slope-intercept form of a line. Where slope = 5/2 and y-intercept = -4
Learn more about the equation of a line and its slope here:
https://brainly.com/question/1884491
#SPJ2
