This lesson will teach you to write the equation of a lie given any two points on that line.
Process:
Step 1: Find the slope of the line.
Step 2: Find the y-intercept of the line.
Step 3: Write the equation of the line using slope-intercept form.
Example:
Write an equation of the line that passes through the points
(3, 1), and (6, -2).
Solution:
Step 1: Find the slope of the line.
Let (X1, Y1) = (3, 1) and (X2, Y2) = (6, -2). Substitute each value into the equation for slope.
The slope of the line is -1.
Step 2: Find the y-intercept of the line.
Select one of the given points, (3, 1) and let x=3, y=1, and m = -1. Substitute each value into the slope-intercept equation.
y = mx + b
1 = -1(3) + b
1 = -3 + b
4 = b
The y-intercept of the line is 4.
Step 3: Write the equation in slope-intercept form.
Using m = -1 and b = 4, substitute into the slope-intercept equation.
y = mx + b
y = -1x + 4
The simplified form of the equation of the line is
y = -x + 4.
Assignment:
Write an equation of the line passing through each pair of points. Write the equation in slope-intercept form.
1. (3, 14) and (1, 4)
2. (-6, -9) and (-5, 10)
3. (12, -7) and (10. -3)
4. (-6, -5) and (2, 3)
5. (4, -2) and (5, 4)
6. (-4, 9) and (-3, 8)
7. (1/2, -1/2) and (1/4, 3/4)
8. (-1, 0) and (-5, -3)
9. (-3, 7) and (1, 7)
10. (1, 2) and (3, 4)
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