Find the equation of the line passing through the points (2, 3) and (4, 5).

Q: Find the equation of the line passing through the points (2, 3) and (4, 5).

Finding the Equation of a Line \nThe equation of a line passing through two points (x1, y1) and (x2, y2) can be found using the point-slope form of a line. The point-slope form is given by: \ny - y1 = m(x - x1) \nwhere m is the slope of the line. Step 1: Find the slope of the line.\nTo find the slope of the line passing through the points (2, 3) and (4, 5), we can use the formula: \nm = (y2 - y1) / (x2 - x1) \nSubstituting the values of the points, we get: \nm = (5 - 3) / (4 - 2) \nSimplifying this expression gives us: \nm = 2 / 2 \nm = 1 Step 2: Find the equation of the line.\nNow that we have the slope of the line, we can use the point-slope form to find the equation of the line. We have: \ny - 3 = 1(x - 2) \nSimplifying this equation gives us: \ny - 3 = x - 2 \nAdding 3 to both sides gives us: \ny = x + 1 \nTherefore, the equation of the line passing through the points (2, 3) and (4, 5) is y = x + 1.

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Finding the Equation of a Line 
The equation of a line passing through two points (x1, y1) and (x2, y2) can be found using the point-slope form of a line. The point-slope form is given by: 
y - y1 = m(x - x1) 
where m is the slope of the line. Step 1: Find the slope of the line.
To find the slope of the line passing through the points (2, 3) and (4, 5), we can use the formula: 
m = (y2 - y1) / (x2 - x1) 
Substituting the values of the points, we get: 
m = (5 - 3) / (4 - 2) 
Simplifying this expression gives us: 
m = 2 / 2 
m = 1 Step 2: Find the equation of the line.
Now that we have the slope of the line, we can use the point-slope form to find the equation of the line. We have: 
y - 3 = 1(x - 2) 
Simplifying this equation gives us: 
y - 3 = x - 2 
Adding 3 to both sides gives us: 
y = x + 1 
Therefore, the equation of the line passing through the points (2, 3) and (4, 5) is y = x + 1.

MP Board · Class 10 · Mathematics · Pair of Linear Equations in Two VariablesFind the equation of the line passing through the points (2, 3) and (4, 5).