1. Sec. 2-2: Linear Equations 9/19/17

2. Linear Function (equation):
A function whose graph is a line.
Dependent Variable: y
“Dependent” since the value of y depends on x.
Independent Variable: x
It depends upon nothing.

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)

4. Standard Form of a Linear Equation: Ax + By = C 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.

5. Slope: given two points (x1, y1) & (x2, y2) …
m = y2 – y = ∆y = “rise”
x2 – x ∆x “run”
Find the slope of the line that goes through the points: (2/3, 1) and (-3, ½)
m = 1 – ½ = ½ = ½
2/ /3 + 9/ /3
m = ½ ● 3/11 = 3/22

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 (b) first
From that point, move according to the slope: “rise”
“run”

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

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)
(x1, y1) are the coordinates; m is the slope
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 stuck on the “STANDARD FORM”. When you need to write an equation you can always use the POINT-SLOPE formula.
y – y1 = m(x – x1)
y – 2 = -3(x + 1)
y – 2 = -3x – 3
Then manipulate the equation to put it in STANDARD FORM.
3x + y = -1

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.

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 to determine the slope.
Use the Point-Slope Formula 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 new 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 new m = -3/2
2. Use y – y1 = m(x – x1) and plug in the new slope and the given point.
y – 9 = -3/2(x + 5) that’s it! {It didn’t specify a certain form.}

14. Assignment: Page 67 #1 – 16