Find the standard form of the equation of the line that passes through (0,1) and (4,6)

Question

asked Apr 20, 2020 141k views

1 Answer

WeiHao · Answer 1 · 2020-04-25T13:44:16+0000

For this case we have that by definition, the standard form of a linear equation is given by:

ax + by = c

By definition, the slope of a line is given by:

$m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}$

We have as data that the line searched goes through the following points:

$(x_ {1}, y_ {1}) :( 0,1)\\(x_ {2}, y_ {2}) :( 4,6)$

Then, the slope is:

$m = \frac {6-1} {4-0}\\m = \frac {5} {4}$

Thus, the equation in the slope-intersection form will be given by:

$y = \frac {5} {4} x + b$

We substitute one of the points to find the cut-off point with the y-axis, that is, "b":

$1 = \frac {5} {4} (0) + b\\b = 1$

Thus, the equation is:

$y = \frac {5} {4} x + 1$

We manipulate algebraically:

$y-1 = \frac {5} {4} x\\4 (y-1) = 5x\\4y-4 = 5x\\-5x + 4y-4 = 0\\-5x + 4y = 4$

ANswer:

The standard form of the requested equation is: