1. Sec. 2-2: Linear Equations

2. Linear Function (equation):
A function whose graph is a line.
Dependent Variable:
(y) Since the value of y depends on(or is determined by) “x”.
Independent Variable: x
“X” controls what happens.

3. Y-Intercept: (0, #)
A point where a line crosses the y-axis.
Found by putting zero in for the x value.
X-Intercept: (#, 0)
A point where a line crosses the x-axis.
Found by putting zero in for the y value.
Given y = 5x + 7 find the intercepts.
The x-Int. is (-7/5, 0) the y-Int. is (0, 7) Video Help

4. Standard Form of a Linear Equation: Ax + By = C No fractions
“A” must be POSITIVE
x & y are on the SAME side of the equation
Finding x- & y-intercepts is easiest when the equation is in this format.
Video Help

5. Slope: m = y1 – y2 = ∆y = “rise” x1 – x2 ∆x “run”
Find the slope of the points: (2, 1) and (-3, ½)
m = 1 – ½ = ½ = 1/2
m = = = Video Help
End of day 1

6. Slope-Intercept Form:
y = mx + b
Where m is the slope and b is the y-intercept
Easy format to graph with:
Graph the y-intercept first
From that point, move according to the slope: “rise”
“run”
Video Help

7. To write an equation with the slope-intercept form, you would need the SLOPE & the y-intercept.
i.e. Write the equation that contains the points (-2, 0) & (0, 5).
*** You would first determine the slope & use the y-intercept (0, 5)
m = 5 – 0 = so y = 5/2x + 5
Video Help

8. 9. Point-Slope Form:
Used to write an equation of a line if you’re given a “point” on the line, and the “slope” of the line.
y – y1 = m (x – x1)
Plug your information into the highlighted variables and solve the equation for the desired format.

9. Write the standard form equation of a line
with slope -3 that goes through the point (-1, 2).
*** Don’t get hung up on the “STANDARD FORM”. . . When you need to write an equation you will always use the POINT-SLOPE formula.
y – y = m(x – x)
y – 2 = -3(x + 1)
y – 2 = -3x – 3
Then manipulate the equation to put it in STANDARD FORM.
3x + y = -1
End of day 2 Video Help

10. Lines that never intersect. Slopes are the same.
Parallel Lines: //
Lines that never intersect.
Slopes are the same.
Perpendicular Lines: ┴
Lines that intersect at 90° angles.
Slopes are OPPOSITE RECIPROCALS.
Identify the following lines as // or ┴ or neither.
Video Help

11. y = 3x – 2
y = 3x -12
// because both slopes are 3
2y = -x + 5
y = 2x + 4
┴ because the 1st slope is -1/2 & the 2nd is 2
3x – 2y = -8
x + y = 1
Neither because the 1st slope is 3/2 & the 2nd is -1

12. Writing equations of // & ┴ lines
Determine the desired slope You may have to manipulate the original equation around to pick off the slope.
Use the Point-Slope Form to write the equation, plugging in the desired slope & the given point.
Put the equation in the desired format.

13. We need a ┴ slope so m ┴ = -3/2
Write an equation of a line ┴ 2x – 3y =7 and that goes through the point (-5, 9).
1. First, determine the current line’s slope:
(solve for y) y = 2/3x - 7/3 so m = 2/3
We need a ┴ slope so m ┴ = -3/2
2. Use y – y = m(x – x) and plug in the new slope and the given point.