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Writing Equations

Other Forms of Linear Equations

Problems

Problems

Horizontal Lines

Horizontal lines have a slope of 0 . Thus, in the slope-intercept equation y = mx + b , m = 0 . The equation becomes y = b , where b is the y -coordinate of the y -intercept.


Example 1: Write an equation for the following line:

Graph of a Line
Since y always takes the value -1 , an equation for the line is y = - 1 .


Example 2: Write an equation for the horizontal line that passes through (6, 2) .

Since the line is horizontal, y is constant--that is, y always takes the same value. Since y takes a value of 2 at the point (6, 2) , y always takes the value 2 . Thus, the equation is y = 2 .

Vertical Lines

Similarly, in the graph of a vertical line, x only takes one value. Thus, the equation for a vertical line is x = a , where a is the value that x takes.


Example 3: Write an equation for the following line:

Graph of a Line
Since x always takes the value 2 = , the equation for the line is x = .


Example 4: Write an equation for the vertical line that passes through (6, 2) .

Since the line is vertical, x is constant--that is, x always takes the same value. Since x takes a value of 6 at the point (6, 2) , x always takes the value 6 . Thus, the equation is x = 6 .

Incidentally, the lines y = 2 and x = 6 are perpendicular to each other. In fact, all horizontal lines y = b are perpendicular to all vertical lines x = a . The usual relationship between the slopes of perpendicular lines does not work here, as we might expect, because the slope of a horizontal line is 0 which has no reciprocal.

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