# 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 (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 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 (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
]