Question

Slope-intercept from two points (1,4) and (2,2)​

Answer 1

`y=-2x+6`

Explanation:

Equation of the line

First, we find the slope of the line.

Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

`\displaystyle m=(y_2-y_1)/(x_2-x_1)`

The two points are (1,4) and (2,2), thus:

`\displaystyle m=(2-4)/(2-1)=(-2)/(1)`

`m=-2`

The equation of a line passing through (h,k) and slope m is:

`y-k=m(x-h)`

`y-4=-2(x-1)`

Note we used the point (1,4). If we used the other point, the result would have been the same. Operating the equation:

`y-4=-2x+2`

Adding 4:

`y=-2x+6`

The slope-intercept form of the line is

`\boxed{y=-2x+6}`