Find the equation, in standard form, of the line passing through the points (-2,1) and (4,2)?
First you need the slope.
slope = (2-1)/4+2) = 1/6
using point slope form:
y - 1 = (1/6)(x + 2)
6y - 6 = x + 2
in standard form
x - 6y = -8
To find the equation of the line passing through the points (-2,1) and (4,2), we can use the point-slope form of the equation of a line.
Step 1: Find the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
m = (2 - 1) / (4 - (-2))
m = 1 / 6
Step 2: Now that we have the slope, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
Using either one of the given points, let's use (-2,1), substitute the values into the point-slope form:
y - 1 = (1/6)(x - (-2))
y - 1 = (1/6)(x + 2)
Step 3: Simplify the equation:
y - 1 = (1/6)(x + 2)
y - 1 = (1/6)x + 1/3
To write the equation in standard form, move all terms to one side of the equation:
(1/6)x - y + 1/3 - 1 = 0
(1/6)x - y + 1/3 - 3/3 = 0
(1/6)x - y - 2/3 = 0
Finally, multiply the entire equation by 6 to eliminate fractions and get the equation in standard form:
6(1/6)x - 6y - 2 = 0
x - 6y - 2 = 0
Therefore, the equation of the line passing through the points (-2,1) and (4,2) in standard form is x - 6y - 2 = 0.
To find the equation of a line in standard form, we need to determine the values of A, B, and C in the general form equation Ax + By = C.
Step 1: Find the slope of the line using the formula:
slope (m) = (y2 - y1) / (x2 - x1),
where (x1, y1) and (x2, y2) are the coordinates of the two points.
Given points: (-2, 1) and (4, 2)
Using the formula:
slope (m) = (2 - 1) / (4 - (-2))
= 1 / 6
Step 2: Use the point-slope form of a line to find the equation, which is given as:
y - y1 = m(x - x1),
where m is the slope and (x1, y1) is any point on the line.
Using the point-slope form with the point (-2, 1):
y - 1 = (1/6)(x - (-2))
= (1/6)(x + 2)
= (1/6)x + 1/3
Step 3: Rearrange the equation to standard form, which is Ax + By = C. Multiply both sides of the equation by 6 to eliminate the fractions:
6(y - 1) = 6(1/6)x + 6(1/3)
6y - 6 = x + 2
x - 6y = -4
Thus, the equation of the line passing through the points (-2,1) and (4,2) in standard form is x - 6y = -4.