Give the points (1, -2) and (-3, 6), derive the the equation of the straight line joining these two points
slope = (6 - -2) / (-3 - 1) = -2
using point-slope ... y + 2 = -2 (x - 1) ... y = -2 x
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To find the equation of a straight line passing through two given points, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where (x1, y1) are the coordinates of one point and m is the slope of the line.
Given the points (1, -2) and (-3, 6), we can proceed as follows:
1. Find the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
m = (6 - (-2)) / (-3 - 1)
= 8 / (-4)
= -2
2. Choose one of the points, such as (1, -2), and substitute the values into the point-slope form:
y - y1 = m(x - x1)
y - (-2) = -2(x - 1)
y + 2 = -2x + 2
y = -2x + 2 - 2
y = -2x
Therefore, the equation of the straight line passing through the points (1, -2) and (-3, 6) is y = -2x.
To derive the equation of the straight line joining two points, we can use the formula for finding the equation of a line given two points, which is:
y - y1 = m(x - x1)
Where (x1, y1) are the coordinates of one point on the line, m is the slope of the line, and (x, y) are the coordinates of any other point on the line.
Step 1: Find the slope (m) of the line
The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Given the coordinates (1, -2) and (-3, 6), we can compute the slope:
m = (6 - (-2)) / (-3 - 1)
= 8 / -4
= -2
So the slope (m) of the line is -2.
Step 2: Choose one of the points (x1, y1) to substitute into the equation.
Let's choose the point (1, -2) as (x1, y1).
Step 3: Substitute the values into the equation.
Using y - y1 = m(x - x1) and substituting the values:
y - (-2) = -2(x - 1)
y + 2 = -2(x - 1)
Step 4: Simplify the equation.
Expanding the brackets:
y + 2 = -2x + 2
Step 5: Rewrite the equation in the standard form.
To convert the equation to the standard form (Ax + By = C), rearrange the equation:
2x + y = 0
Therefore, the equation of the straight line joining the points (1, -2) and (-3, 6) is 2x + y = 0.