For this case we have that by definition, the standard form of a linear equation is given by:
[tex]ax + by = c[/tex]
By definition, the slope of a line is given by:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]
We have as data that the line searched goes through the following points:
[tex](x_ {1}, y_ {1}) :( 0,1)\\(x_ {2}, y_ {2}) :( 4,6)[/tex]
Then, the slope is:
[tex]m = \frac {6-1} {4-0}\\m = \frac {5} {4}[/tex]
Thus, the equation in the slope-intersection form will be given by:
[tex]y = \frac {5} {4} x + b[/tex]
We substitute one of the points to find the cut-off point with the y-axis, that is, "b":
[tex]1 = \frac {5} {4} (0) + b\\b = 1[/tex]
Thus, the equation is:
[tex]y = \frac {5} {4} x + 1[/tex]
We manipulate algebraically:
[tex]y-1 = \frac {5} {4} x\\4 (y-1) = 5x\\4y-4 = 5x\\-5x + 4y-4 = 0\\-5x + 4y = 4[/tex]
ANswer:
The standard form of the requested equation is:
[tex]-5x + 4y = 4[/tex]
