Linear Equations. What makes a linear equation LINEAR? An equation in one or more variables, each...
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Transcript of Linear Equations. What makes a linear equation LINEAR? An equation in one or more variables, each...
What makes a linear equation LINEAR? An equation in one or more
variables, each with an exponent of ONLY 1, where these variables are only added or subtracted.
So with that definition Which of these equations are linear? x+y = 5 2x+ 3y = 4 7x-3y = 14 y = 2x-2
y=4
x2 + y = 5 x = 5
xy = 5 x2 +y2 = 9 y = x2
3
y
So with that definition Which of these equations are linear?
x+y = 5 2x+ 3y = 4 7x-3y = 14 y = 2x-2
y=4
x2 + y = 5 x = 5
xy = 5 x2 +y2 = 9 y = x2
3
y
Linear Not Linear
Intercepts – where the line crosses the axes.y
x
y
x
Line A Line B
y-intercept=4
x-intercept=-5y-intercept=-5
x-intercept=-3
Intercepts are actually points in the coordinate system.
y
x
y
x
Line A Line B
y-intercept=(0,-5)
x-intercept=(-3,0)
x-intercept=(-5,0)
y-intercept=(0,4)
Linear Equations – What you should be able to identify for all lines. The Equation Form Direction Slope y-intercept x-intercept Parallel Slope Perpendicular Slope
Given our 4 example equations identify all of the following…
The Equation Form Direction Slope y-intercept x-intercept Parallel Slope Perpendicular Slope
1. y = ½ x + 5
2. y = -3x – 7
3. 3x – 2y = 9
4. 4x + 2y = 16
y = ½ x + 5 The Equation Form Direction Slope y-intercept x-intercept Parallel Slope Perpendicular Slope
1. Slope intercept
2. Rising
3. ½
4. 5
5. -5/(½) = -10
6. ½
7. -2
y = -3x – 7 The Equation Form Direction Slope y-intercept x-intercept Parallel Slope Perpendicular Slope
1. Slope intercept
2. Falling
3. -3
4. -7
5. - -7/(-3) = -7/3
6. -3
7. -7
3x – 2y = 9 The Equation Form Direction Slope y-intercept x-intercept Parallel Slope Perpendicular Slope
1. Standard
2. Rising
3. 3/2
4. -4.5 or 9/2
5. 3
6. 3/2
7. -2/3
4x + 2y = 16 The Equation Form Direction Slope y-intercept x-intercept Parallel Slope Perpendicular Slope
1. Standard
2. Falling
3. -2
4. 8
5. 4
6. -2
7. 1/2
What if you are just given two points on a line? The slope formula
m =
Similar to Point-Slope Form
y – y1 = m(x – x1) or y2 – y1 = m(x2 – x1)
y2 – y1
x2 – x1
Now substitute the slope and one point into the slope intercept form y = mx + b m = 5/3 point (6,6)
6 = (5/3)(6 + b) 6 = 10 + (5/3)b -4 = (5/3)b -12/5 = b
Linear equation is y = (5/3)x – 12/3