Finding the Equation of a Line
To find the equation of a line passing through two points, $(x_1, y_1)$ and $(x_2, y_2)$, we first determine the slope ($m$) and then the y-intercept ($c$) to form the equation $y = mx + c$. The given points are (1, 2) and (3, 8).
1. Calculate the Slope ($m$)
The slope is calculated using the formula:
$m = \frac{y_2 - y_1}{x_2 - x_1}$
Substitute the coordinates of the given points:
$m = \frac{8 - 2}{3 - 1} = \frac{6}{2} = 3$
The slope ($m$) is 3.
2. Determine the Y-intercept ($c$)
Use the slope ($m=3$) and one of the points (e.g., (1, 2)) in the slope-intercept form ($y = mx + c$):
$2 = 3(1) + c$
$2 = 3 + c$
Solve for $c$:
$c = 2 - 3 = -1$
The y-intercept ($c$) is -1.
3. Write the Equation
Substitute the calculated slope ($m=3$) and y-intercept ($c=-1$) into the slope-intercept form $y = mx + c$:
$y = 3x - 1$
This is the equation of the line passing through the points (1, 2) and (3, 8).
Similar Questions
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Important Questions from Coordinate Geometry
What is the reflection of the point (-1, 5) in the line x = 1?
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Find the co-ordinates of the centroid of a triangle whose vertices are A(1, 4), B(7, 8) and C(10, 12).
- If x² + y² - 12x + 18y + 117 = 0, then the value of x² + y² is:
