Chapter 3

Chapter 3

Slope and Equations of Lines​

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Slope of Line

​The slope of a line is the steepness of a line. It tells us how fast our line is rising (or falling).

We can find slope two main ways:​

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On a graph, we can use Rise over Run

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When only given numbers we can use the slope equation:​

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​Ex: Find the slope of the line two different ways

​A. Find the slope of a line given the points (1,3) and (2,6)

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B. ​Find the slope of a line given the points (-11,8) and (4,9)

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Slope Intercept From

​Slope Intercept Form is the most common equation we can use to represent a line.

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y = mx + b

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Where m is your slope and b is your y intercept and x and y are your coordinates on the line.​

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​Ex: Write the equations 2x + 4y = 8 in slope intercept form

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Ex: Identify the slope and y intercept in the equation:

y = -3x -4​

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​A. Convert to slope intercept form:

10x - 5y = 25

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B. Identify the slope and y intercept in the equation:

y = 7x - 8​

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Point Slope Form:

​Point Slope From is the second most common way to write the equation of a line.

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To write in point slope form we will need two points and the slope:

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(y₂-y₁) = m(x₂-x₁)​

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​Ex: Use the points (2,1) and (10,5) to write an equation of a line in point slope form.

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​A. What is the equation in point slope for of a line with points (5,6) and (-5,-6)?

How to find x and y intercepts:

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​The x intercpt is where the line crosses the x axis, or what x is when y is 0.

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The y intercept is where the line crosses the y axis, or what y is when x is 0.​

​Ex: Find the x and y intercepts in the equation 3x + 2y = 6

​A. 2y + 8x = 16

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B. y = 3x + 9​

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Translations of Absolute Value Graphs

​A Translation is a slide up and down (change in y) left or right (change in x).

Up and Right are positive.

Down and Left are negative.​

When we are moving right (or left), we will ​add (or subtract) the amount inside the absolute value sign.

When we are moving up (or down), we will add (or subtract) the amount outside the absolute value sign.​

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​Ex: Perform the following operations on the equation y = |x|

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1. ​2 units up

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2. 3 units left

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3. 4 units down

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4. 5 units right​

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​Perform the following operations on y = |x|

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A. 2 units down

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B. 5 units to the right​

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How do perpendicular and parallel lines relate to slope?

If two lines are parallel, then they will have the same slope.

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If two lines are perpendicular, then they will have​ opposite reciprocals of the slope. [Meaning the slope flips upside down and changes sign (positive and negative)]

What is the slope of a line that is parallel to y = 3x + 4?

What is the slope of a line that is perpendicular to y = 2x -5?​

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​Ex: What is the equation of a line that is parallel to y = 2x + 5 and passes through the point (1,5)?

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Ex: What is the equation of a line that is perpendicular​ to y = -1/2x + 4 and passes through the point (2,4)?

​A. What is the equation of a line that is parallel to y = 4x - 5 and passes through the point (-2,1)?