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 Depdendent Variable

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 Dependent Variable

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# Writing Equations for Lines Using Sequences

I. If we are given the slope m and the y-intercept b or (0, b) we can fill in these values to WRITE the equation for the line as a function in the slope-intercept form:

y = m x + b

Example 1:

1. Write the equation y = m x + b for the straight line with slope of - 2 and y-intercept of 3.

Use the fact that the slope is m = - 2 and the y-intercept 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 (x1, y1) use the values for m, x1, y1 as the replacement values in the equation:

y = m(x â€“ x1) + y1 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 y-intercept 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 (x1, y1) and the slope is 3 means: m = 3, x1 = 2 and y1 = -2

substitute these in the equation y = m(x â€“ x1) + y1 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 ]