How can I find the equation in standard form using only integers for the line through (-1,-3) and (2,-1)?
first find the slope
slope (-3 + 1)/(-1-2) = 2/3
using the point (2,-1)
y+1 = (2/3)(x-2)
3y+3 = 2x-4
2x - 3y = 7
or
2x - 3y - 7 = 0 , depending what your course defines as "standard from"
The slope is m = (-1 +3)/(2+1) = 2/3
So the equation in standard form is
y = (2/3)x + b
You still need to determine the constant b. Require that
-1 = (2/3)*2 +b
b = -7/3
Therefore
y = (2/3)x - 7/3
If you want integer coefficients only, you will have to write it as
3y = 2x - 7
Ax+By=C
To find the equation of a line in standard form using only integers, you can follow these steps:
Step 1: Find the slope (m) of the line.
The slope (m) of a line passing through two points (x₁, y₁) and (x₂, y₂) can be calculated using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
In this case, the two given points are (-1, -3) and (2, -1). Plugging these values into the formula, we get:
m = (-1 - (-3)) / (2 - (-1))
= (-1 + 3) / (2 + 1)
= 2 / 3
So the slope of the line is 2/3.
Step 2: Use the slope-intercept form (y = mx + b) to find the equation.
The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.
We already know the slope (m = 2/3). Now, to find the y-intercept, we can choose one of the given points and substitute its coordinates into the equation.
Let's take the point (-1, -3):
y = mx + b
-3 = (2/3)(-1) + b
-3 = -2/3 + b
To solve for b, we can rearrange the equation:
b = -3 + 2/3
b = -9/3 + 2/3
b = -7/3
So the y-intercept (b) is -7/3.
Step 3: Write the equation in standard form.
Now that we have the slope (m = 2/3) and y-intercept (b = -7/3), we can substitute these values into the slope-intercept form to get the equation in standard form.
y = mx + b
y = (2/3)x - 7/3
To eliminate fractions, we can multiply both sides of the equation by 3:
3y = 2x - 7
Finally, rearrange the equation in standard form by moving all the terms to one side:
2x - 3y = 7
Therefore, the equation of the line passing through the points (-1, -3) and (2, -1) in standard form using only integers is 2x - 3y = 7.