Find the equation of the line through the given pair of
points in standard form using only integers. 3) (5, 2) and (-1, 6)
(-1,6), (5,2).
m = (2-6)/(5-(-1)) = -4/6 = -2/3.
Y = mx + b.
6 = (-2/3)(-1) + b,
b = 6-2/3 = 18/3-2/3 = 16/3.
y = -2x/3 + 16/3,
2x/3 + y = 16/3,
Multiply Eq. by 3:
2x + 3y = 16. Std. form.
To find the equation of a line through two given points in standard form using integers, we can use the point-slope form of a linear equation and then convert it into standard form.
1. First, let's find the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (5, 2) and (x2, y2) = (-1, 6)
Substituting the values into the formula:
m = (6 - 2) / (-1 - 5)
= 4 / (-6)
= -2/3
2. Now that we have the slope, we can use the point-slope form of the equation, which is:
y - y1 = m(x - x1)
where (x1, y1) is either of the given points.
Let's use (5, 2) as (x1, y1):
y - 2 = -2/3(x - 5)
3. Next, simplify the equation:
y - 2 = -2/3x + 10/3
4. To convert the equation to standard form, eliminate fractions by multiplying through by the common denominator (3):
3y - 6 = -2x + 10
5. Rearrange the equation so that the x and y terms are on the same side, and the constant term is on the other side:
2x + 3y = 16
Hence, the equation of the line passing through the points (5, 2) and (-1, 6) in standard form using only integers is 2x + 3y = 16.