Find the equation of the line passing through the points A(1, -2) and B(3, 2).

Q: Find the equation of the line passing through the points A(1, -2) and B(3, 2).

Equation of a Line Passing Through Two Points \nWhen two points are given, we can find the equation of the line passing through them using the formula for the slope of a line. The formula for the slope (m) of a line passing through two points (x1, y1) and (x2, y2) is given by: \nm = (y2 - y1) / (x2 - x1) \nUsing this formula, we can find the slope of the line passing through points A(1, -2) and B(3, 2). \nm = (2 - (-2)) / (3 - 1) \nm = 4 / 2 \nm = 2 \nNow that we have the slope, we can use the point-slope form of the equation of a line, which is given by: \ny - y1 = m(x - x1) \nUsing this formula, we can find the equation of the line passing through point A(1, -2) with a slope of 2. \ny - (-2) = 2(x - 1) \ny + 2 = 2x - 2 \ny = 2x - 4 \nTherefore, the equation of the line passing through points A(1, -2) and B(3, 2) is y = 2x - 4.

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Accepted Answer

Equation of a Line Passing Through Two Points 
When two points are given, we can find the equation of the line passing through them using the formula for the slope of a line. The formula for the slope (m) of a line passing through two points (x1, y1) and (x2, y2) is given by: 
m = (y2 - y1) / (x2 - x1) 
Using this formula, we can find the slope of the line passing through points A(1, -2) and B(3, 2). 
m = (2 - (-2)) / (3 - 1) 
m = 4 / 2 
m = 2 
Now that we have the slope, we can use the point-slope form of the equation of a line, which is given by: 
y - y1 = m(x - x1) 
Using this formula, we can find the equation of the line passing through point A(1, -2) with a slope of 2. 
y - (-2) = 2(x - 1) 
y + 2 = 2x - 2 
y = 2x - 4 
Therefore, the equation of the line passing through points A(1, -2) and B(3, 2) is y = 2x - 4.

MP Board · Class 10 · Mathematics · Coordinate GeometryFind the equation of the line passing through the points A(1, -2) and B(3, 2).