Question 1206892
the points are (-2,2), (5,1)
let x1,y1 = -2,2 and x2,y2 = 5,1
slope = (y2-y1)/(x2-x1) = (1-2)/(5+2) = -1/7
use one of the points to get the y-intercept.
general slope intercept form equation is y = mx + b
m is the slope
b is the y-intercept
when the slope is -1/7, equation becomes y = -1/7 * x + b
use (5,1) coordinate and replace y with 1 and x with 5 to get:
1 = -1/7 * 5 + b
solve for b to get:
b = 1 + 5/7 = 12/7
equation becomes y = -1/7 * x + 12/7.
that's the slope intercept form of the equation.
to get the standard form, do the following:
add -1/7 * x to both sides of the equation to get 1/7 * x + y = 12/7
multiply both sides of the equation by 7 to get x + 7y = 12
that's the standard form of the equation.


here's the graph.


<img src = "http://theo.x10hosting.com/2024/041201.jpg">


note that the standard form and the slope intercept form of the equation draw the same line.
that's because they're equivalent.


the two speciied points are on the line.
they are (-2,2) and (5,1)
the slope intercept is (0,1.714) where 1.714 represents the fraction 12/7.