Write a Linear Equations

Write a Linear Equations

This is a NEW topic. PLEASE make sure you take complete notes. You will need them at the end of the lesson to answer questions and you will need to submit them when done.

Multiple Choice

What is a linear equation anyway?

• Mrs. Fox's science equation.

• An equation that creates a parabola.

• An equation that creates a straight line.

• A equation that does not have a slope.

Multiple Choice

Is this relationship linear? How do you know?

• No, because when I divide each y by its corresponding x is not equal.

• Yes, because it looks like it would be.

• No, because there is not a constant rate of change.

• Yes, because there is a constant rate of change.

Rate of change.

This is a friendly reminder of rate of change also known as slope,

Multiple Choice

What is the slope of the related graph?

• m = 11

• m = 9

• m = -9

• m = 12

How did we get nine?

• Pick two sets of points. For example (1,13) and (2, 22)

• Label them y₁ , y₂ and x_1, x₂

• Subtract the y's in the numerator and the x's in the denominator.

• Slope Equation: m = y₂ - y₁ = x₂ - x₁

• m = 22 - 13 / 2 - 1

• Slope = 9/1 or 9

Multiple Choice

Now lets find the y-intercept. You have a slope of 9 and you can pick any of the points. So you have a slope of 9 and lets use the point (1, 13). Hint : y = mx + b

• b = 4

• b = 3

• b = 2

• b = 1

How did we find b = 4?

• m=9, x=1, y=13

• y=mx+b

• 13 = 9(1) + b

• 13 = 9 + b

• subtract 9 from both sides.

• 4 = b

Multiple Choice

So the equation then is?

• 13 = 9(1) + 4

• y = mx + b

• 13 = x +4

• y = 9x + 4

Point Slope Formula

New material! This is another format to write a linear equation. If you have not figured it out it involves a point and the slope!

Point Slope Formula Explained.

Using a point and slope to find a formula.

Example 1 - Leaves the equation in point slope form.

Example 2 - Converts the equation into slope y-intercept form.

EXAMPLE 1 - Given the point and slope below find the equation of the line in point slope form.

(3,5) m = 7

• Write Equation: y - y₁ = m(x - x₁)

• Substitute point and slope into equation.: y - 5 = 7(x - 3)

• DONE!

EXAMPLE 2 - Given the point and slope below find the equation of the line in slope intercept form. (y = mx + b)

(3,5) m = 7

• Write Equation: y - y₁ = m(x - x₁)

• Substitute point and slope into equation.: y - 5 = 7(x - 3)

• Distribute 7 : y - 5 = 7x - 21

• Add 5 to both sides : y = 7x - 16

• DONE!

Multiple Choice

Lets try one!

Write an equation in point-slope form for the line that passes through (1,2) and has a slope of - 1/2.

Remember point slope form is: y - y1 = m(x - x1)

• y + 1 = -1/2(x - 2)

• y - 2 = -1/2(x +(-1))

• y - 2 = -1/2(x - 1)

• y + 2 = -1/2(x + 1)

Multiple Choice

Write the equation of the line in Point-Slope form that goes through the point (10,5) and has a slope of -3

• y - 5 = -3(x - 10)
• y= -3x + 35
• y + 5= -3(x + 10)
• y= -3x - 35

Multiple Choice

Write the equation in point-slope form of the line that passes through the given point and has the given slope. (watch your signs)

(4, -7); m = -1/4

• y + 7 = -1/4(x - 4)

• y - 4 = -1/4(x + 7)

• y + 7 = 4(x - 4)

• y - 7 = -1/4(x - 4)

Multiple Choice

Write an equation

m = 5 through (-1, -3)

• y = 5x + 2

• y = 5x - 5

• y = -5x + 2

• y = 2x - 5