1. 1.4 Lines, writing, finding slopes and intersections Part I
Line on a graph: Count up(+)/down(-) and right(+)/left(-) from one point on the line to another and simplify.
Example: Practice:
-3/2 y goes down 3 as x goes right 2
2/3 y goes up 2 while x goes right 3

2. 1.4 Lines, writing, finding slopes and intersections Part I
Given points: use the equation (difference in y’s over difference in x’s)
Example: Practice:
(-2,1); (0,0) (-2,3); (2,1)

3. 1.4 Lines, writing, finding slopes and intersections Part I
Given an equation: solve for y, then the coefficient of x is the slope.
Example: Practice:
y – 3 = 2x y = 2x + 6
y = 2x + 8
m = 2
slope
y = 2/3 x + 2
m = 2/3
slope

4. Special cases:
Vertical line: The equation is written as x = a (there is no y because it never crosses the y axis) the slope is undefined.
x = 5 is a vertical line going through the x axis at 5 and the slope is undefined because the denominator is 0
Horizontal: The equation is written as y = b (there is no x because it never crosses the x axis) the slope is 0
y = -3 is a horizontal line going through the y axis at -3 and the slope is 0 because the numerator is 0.

5. Writing the equation of a line:
3 formulas:
Slope intercept form: y = mx + b
slope y value of the y intercept point
Example: write the equation of the line with a slope of -3 and a y-intercept at 4.
y = -3x + 4
Practice: write the equation of a line through the points (0,3); (4,4)
First find the slope: the y-intercept is 3 since one of the points has a 0 for x the y value must be the y intercept.
y = ¼ x + 3

6. Writing the equation of a line:
slope
Point slope form: y – y1 = m(x – x1)
y value of x value of a
a point point
Example: write the equation of a line whose slope is – ½ and goes through a point (4, -2).
y - -2 = - ½ (x – 4) ; y + 2 = - ½ (x – 4)
Practice: write the equation of the line that goes through (2,5) & (-3,4)
Find slope then use either point to finish the equation.
y – 5 = 1/5(x – 2)

7. Standard form:
Ax + By = C
Conditions: A has to be positive (coefficient of x)
A,B,C must be integers.
Example:
y = ½ x -4
2y = x – 8
-x +2y = -8
X – 2y = 8

8. Comparisons of slopes:
// parallel lines must have the same slope but a different y-intercept
Example: write the equation of a line Parallel to the line y = - ¼ x + 9 and through point (-1,7).
Perpendicular lines must have opposite and reciprocal slope.
(sign) (flip)
Example: write the equation of a line perpendicular to the line
y + 2 = 3/2 (x – 4) and through point (0,-3).
Since the line is parallel the slope must be the same – ¼ and using point (-1,7) the equation is y – 7 = - ¼ (x + 1)
Since the line is perpendicular the slope is opposite and reciprocal so it must be – 2/3 and using point (0,-3) the equation is y = -2/3 x – 3

9. Practice:
Write the equation of the line with the given properties using either form.
#51) Slope = -3 ; y-intercept = 3
#63) Parallel to the line x = 5; containing the point (4,2)
Find the slope and y-intercepts and graph
#78)-x + 3y = 6
y = -3x + 3
x = 4
m = 1/3 (0, 2)