1. ALGEBRA II HONORS/GIFTED SECTION 2-4 : MORE ABOUT LINEAR EQUATIONS@
SECTION 2-4 : MORE ABOUT LINEAR EQUATIONS

2. Show that m is the slope in y = mx + b.
Given (x1, y1) and (x2, y2) are two points on a line.
y2 = mx2 + b
y1 = mx1 + b
y2 – y1 = mx2 – mx1 (subtract)
y2 – y1 = m(x2 – x1) (factor)
(divide by x2 - x1)

3. FORMULAS TO KNOW : Slope-Intercept Form y = mx + b
Standard Form Ax + By = C
no fractions, A > 0
Point-Slope Form y - y1 = m(x - x1)
Slope

4. Write the equation of the line in slope-intercept form of the line described.
(x1, y1) (x2, y2)
Now, use point-slope form to complete the problem.
1) (2, 7) and (4, 10)
First, find the slope.
y – y1 = m(x – x1)
Note : You can use either point for x1 and y1.

5. 2) (-2, -4) and (-5, -10) (Write in Standard Form too)

6. 6) Contains (-2, -1) and has a slope of
Graphing calculator exercise for parallel and perpendicular lines.

7. PARALLEL LINES : never intersect. They have the same slope.
PERPENDICULAR LINES : meet at right angles. Their slopes are opposite reciprocals. The product of their slopes is -1 (except for horizontal and vertical lines).

8. Write the equation of the line in slope-intercept form of the line described.
7) Contains (5, 8) and is parallel to y = 7x – 6
Parallel lines have the same slope. So, the slope of the line we want is 7.
Now, use point-slope form.
y – y1 = m(x – x1)
y – 8 = 7x - 35
y – 8 = 7(x – 5)
y = 7x - 27

9. Transform to slope-intercept form.
Therefore, from Standard Form :
the slope is
the y-intercept is

10. ALGEBRA II HONORS/GIFTED - SECTION 2-4 (More About Linear Equations)
8) Contains (-3, 0) and is parallel to 2x + 5y = 9
Using our short cut : m = =
y – y1 = m(x – x1)

11. 9) Contains (-4, 6) and is perpendicular to
Contains (0, 8) and is perpendicular to x – 2y = 1
11) Is horizontal and contains (-8, 9)
12) Is vertical and contains (4, 6)
13) Has x-intercept 5 and slope

12. Another way to handle perpendicular lines.
Write the equation of the line in Standard Form of the line that contains (6, -3) and is perpendicular to x – 5y = 8.
5x + 3y = c Switch the coefficients of x and y, switch the sign in the middle, put c on the right side.
5(6) + 3(-3) = c Substitute 6 for x and -3 for y.
30 + (-9) = c
5x + 3y = 21
= c

13. Write the equation in Standard Form of the line that contains (-5, -1) and perpendicular to 2x + 7y = 3.

14. We’ll end on a sad note!