Lines and Equations
Given the slope ,m, and a point P(x_{1} , y_{1}) use the modified pointslope formula : y = m(x − x_{1} ) + y_{1}
y = m(x − x_{1} ) + y_{1}
⇒ Substitute the values for m and the point P(x_{1} , y_{1}) then remove parentheses and collect like terms to
find the equation in the yintercept form:
y = mx +b
The modified pointslope form: y = m(x − x_{1 }) + y_{1} becomes the yintercept form: y = mx +b
where b = [ y_{1} − mx_{1} ]
Examples:
Write an equation of the line that contains the indicated point(s) and meets the indicated
condition(s). Write the final answer in yintercept form: y = mx +b
#1. P(0, 4), m =  2; ⇒ y = mx + b for the slope (m) and yintercept (b = y_{0}).
Substituting directly : b = 4 y = (2) x + (4) ∴ y =  2x + 4
#2. P( 2, 4), m = 3/2; ⇒ y = m(x − x_{1} ) + y_{1} m = 3/2 and P(x_{1} , y_{1}) → x_{1} =  2, y_{1}=  4
⇒ y = 3/2 [x − ( 2)]+ ( 4) or y = 3/2 x + [(3/2)(+2)+ (4)] or y = 3/2 x + [ 3 − 4]
∴ y = 3/2 x â€“1 b =  1
#3. P(2,3); m = 0 [horizontal] (y = b) Lines that are horizontal go through y = y_{1} ∴ y =  3
#4. Given points: (3, 2), (5,  3) Find Dy and Dx directly from the table or the points.
m =  5/2 x_{1}=3, y_{1}=2 ⇒ y = 5/2 [x  (3)] + (2) or b = 19/2
. ∴ y =  5/2 x + 19/2
#5. Graph
, for b = 3, b = 0, b = 3 or b = {3, 0, 3} on the same coordinate system.
Plot each yintercept (0,b) and use
the slope m = 1/2 to graph the lines.
The lines have the same slope so they are parallel.
