An equation whose graph is a line is called a linear equation. Linear equations may contain one or more variables with no variable having an exponent other that 1.
For example:
Student Activity
Check the box next to each equation if it is linear. If it is not linear, explain why.
1.
2. x-8y=15
3. f(x)=2x-6
4.
5.
6. y=4
A function is linear if it can be defined by f(x) = mx + b, where m and b are real numbers.
Given 10x - 2y = 20, the slope-intercept form of the equation is y = 5x - 10.
Write an equation in y = mx + b form for the line that satisfies each of the following conditions.
7. 2x - 2y = 4
8. 6y = 3x - 12
9. 5x - y = 10
In the equation y = mx + b, b is the y-intercept (the point where the line crosses the y-axis).
Finding the y-intercept
Sometimes it is necessary to determine the y-intercept from other information about the line.
Line 1 : m = and passes through (6, 4). Using y = mx + b:
4 = (6) + b
b = 1
so the equation for Line 1 would be y = x + 1.
Line 2 : passes through (6, 1) and (8, -4).
Using the point (6, 1) and y = mx + b,
1 = (6) + b
b = 16
so the equation for Line 2 would be y = x + b.
Remember: Parallel lines have the same slope and perpendicular lines hav slopes that are opposite reciprocals.
Line 3 : passes through (-2, 0) and is perpendicular to the line y = -3x + 7
0 = (-2) + b
b =
so the equation for Line 3 would be y = x + .
Write an equaiton in y = mx + b form for each line that satifies the given conditions.
10. Line A
-5y = 3x - 30
11. Line B
and passes through (2, -3)
12. Line C
passes through (-1, -1) and (8, -1)
13. Line D
passes through (4, 2) and is parallel to y = 2x - 4
14. Line E
x-intercept = -3 and the y-intercept = 6
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