For this case we have that by definition, the equation of a line of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut-off point with the y axis
While the point-slope equation of a line is given by:
[tex]y-y_ {0} = m (x-x_ {0})[/tex]
Where:
m: It's the slope
[tex](x_ {0}, y_ {0}):[/tex]It is a point through which the line passes
In this case we have a line through:
(8,4) and (0,2)
Therefore, its slope is:
[tex]m = \frac {2-4} {0-8} = \frac {-2} {- 8} = \frac {1} {4}[/tex]
Its point-slope equation is:
[tex]y-4 = \frac {1} {4} (x-8)[/tex]
Then, we manipulate the expression to find the equation of the slope-intersection form:
[tex]y-4 = \frac {1} {4} x- \frac {8} {4}\\y-4 = \frac {1} {4} x-2\\y = \frac {1} {4} x-2 + 4\\y = \frac {1} {4} x + 2[/tex]
Therefore, the cut-off point with the y-axis is [tex]b = 2[/tex]
ANswer:
[tex]y = \frac {1} {4} x + 2[/tex]
