What is the equation for (1/2,2) (-3, -1) in standard form?

Question

asked Jan 28, 2020 172k views

1 Answer

Tpunt · Answer 1 · 2020-02-02T06:24:46+0000

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

ax + by = c

On the other hand, we have that the equation of a line in 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 have two points:

$(x_ {1}, y_ {1}): (\frac {1} {2}, 2)\\(x_ {2}, y_ {2}): (-3, -1)$

We find the slope of the line:

$m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-1-2} {- 3- \frac {1} {2}} = \frac {-3} {- \frac {7} {2}} = \frac {6} {7}$

Thus, the equation is of the form:

$y = \frac {6} {7} x + b$

We substitute one of the points and find "b":

$-1 = \frac {6} {7} (- 3) + b\\-1 = - \frac {18} {7} + b\\-1+ \frac {18} {7} = b\\b = \frac {-7 + 18} {7}\\b = \frac {11} {7}$

Finally, the equation is:

$y = \frac {6} {7} x + \frac {11} {7}$

We convert the equation to the standard form:

$y- \frac {11} {7} = \frac {6} {7} x\\7 (y- \frac {11} {7}) = 6x\\7y-11 = 6x\\-6x + 7y = 11\\6x-7y = -11$

ANswer: