How do you write an equation in standard form for a line passing through (–1, 2) and (3, 4)?

Question

Eva Abramson · Accepted Answer

First find the slope of the line. This is (change in #y#) / (change in #x#).

For your example:

slope #= (Delta y)/(Delta x) = (4 - 2)/(3 - (-1)) = 2 / 4 = 1/2#

Slope intercept form is #y = mx + c# where #m# is the slope and #c# the intercept.

To calculate #c# we can subtract #mx# from both sides to get:

#c = y - mx#.

We know #m=1/2# and we have two example points that satisfy the equation of the line we're aiming for. Let us use #(-1, 2)#...

#c = y - mx = 2 - (1/2*-1) = 2+1/2 = 5/2#

So the equation of our line is:

#y = 1/2x + 5/2#

Isaiah Anthony · Answer

undefined To write an equation in standard form for a line passing through the points (-1, 2) and (3, 4), you first need to find the slope of the line using the formula: $m = \frac{{y_2 - y_1}}{{x_2 - x_1}}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two points.

Using the given points (-1, 2) and (3, 4):
$m = \frac{{4 - 2}}{{3 - (-1)}} = \frac{2}{4} = \frac{1}{2}$

Once you have the slope, you can use either of the two points and the slope to write the equation in point-slope form: $y - y_1 = m(x - x_1)$.

Let's use the point (-1, 2):
$y - 2 = \frac{1}{2}(x - (-1))$

Simplify:
$y - 2 = \frac{1}{2}(x + 1)$
$2y - 4 = x + 1$
$x - 2y = -5$

Thus, the equation in standard form is $x - 2y = -5$.

Ethan Adkins · Answer

undefined To write an equation in standard form for a line passing through the points (-1, 2) and (3, 4), follow these steps:

1. Calculate the slope ($m$) of the line using the formula:
   $m = \frac{{y_2 - y_1}}{{x_2 - x_1}}$

2. Once you have the slope, use one of the points and the slope in the point-slope form of the equation of a line:
   $y - y_1 = m(x - x_1)$

3. Substitute the coordinates of one of the points and the calculated slope into the point-slope form.

4. Simplify the equation obtained in step 3 into standard form:
   $Ax + By = C$, where $A$, $B$, and $C$ are integers and $A$ is positive.

5. Ensure that all coefficients are integers and $A$ is positive. If needed, multiply through by a common factor to achieve this.

Following these steps, you can find the equation of the line passing through the given points.