Question

Through (0,2) and (4,1) write the slope intercept form of the equation of the line

Answer 1

y= -1/4x+2

Explanation:

use the slope formula to get the slope: y2-y1/x2-x1 or 1-2/4-0 subtract to get -1/4 that is the m(slope)*x in y=mx+b now for b it is the point in which x=0 so the first point has x=0 and it's y is 2 so b is 2. put it together to get y=-1/4x+2

Answer 2

For this case we have that the equation of a line of the slope-intersection form is given by:

`y = mx + b`

Where:

m: It's the slope

b: It is the cut-off point with the y axis

We found the slope:

`(x1, y1) :( 0,2)\\(x2, y2) :( 4,1)\\m = \frac {y2-y1} {x2-x1} = \frac {1-2} {4-0} = \frac {-1} {4} = - \frac {1} {4}`

Thus, the equation is of the form:

`y = - \frac {1} {4} x + b`

We find b, substituting any of the points:

`2 = - \frac {1} {4} (0) + b\\b = 2`

Finally, the equation is:

`y = - \frac {1} {4} x + 2`

ANswer:

`y = - \frac {1} {4} x + 2`