Writing Equations for Lines Using Sequences
I. If we are given the slope m and the yintercept b or (0, b) we can fill in these values to
WRITE the equation for the line as a function in the slopeintercept form:
y = m x + b
Example 1:
1. Write the equation y = m x + b for the straight line with slope of  2 and yintercept of 3.
Use the fact that the slope is m =  2 and the yintercept is b = 3.
⇒ Write: m = __ 2__ and b = __3__
EQUATION: y = m x + b: or y = 2x + 3 .
II. Given the slope m and any point (x_{1}, y_{1}) use the values for m, x_{1}, y_{1} as the
replacement values in the equation:
y = m(x â€“ x_{1}) + y_{1} and simplify to y = m x + b.
Then WRITE the values for m and b. and the equation y = m x + b
Example 2:
2. Find the yintercept and write the equation y = m x + b of the line with a slope of 3 that
passes through the point (2,  2).
Since the point (2,  2) is (x_{1}, y_{1}) and the slope is 3 means: m = 3, x_{1} = 2 and y_{1} = 2
substitute these in the equation y = m(x â€“ x_{1}) + y_{1} and simplify to y = m x + b.
or y = (3)(x â€“ 2) + (2 ) then y = 3x â€“ 6 + (2 )
⇒ m = 3 and b = 8 EQUATION y = m x + b: y = 3x â€“ 8
[Check point (2, 2): (2) = 3 Â·( 2) â€“ 8 = 2
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