1.08 Writing Equations of Lines

Learn

Slope-Intercept Form

There will be three types of problems illustrated in the first part of this lesson. You will review:

• How to write an equation of a line given the slope and the y-intercept.
• How to write an equation of a line given the slope and a point of the line
• How to write an equation of a line given two points on the line.

Let's first review how to write the equations in slope-intercept form.

Line Given Slope and y-Intercept

Question: How do I write an equation of a line when given the slope and the y-intercept in slope-intercept form?

Answer: Use the slope intercept form of an equation. y= mx + b where m is the slope and b is the y-intercept

Example #1

Open Write the equation of a line Given the slope and y-intercept Example 1 in a new tab

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Example #2

Open Write the equation of a line Given the slope and y-intercept Example 2 in a new tab

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Line Given Slope and Point

Question: How do I write an equation of a line when given the slope and a point on the line in slope-intercept form?

Answer: Use the point-slope form of an equation of a line: y − y₁ = m (x − x₁)

Watch Write the equation of a line given the lope and a point on the line.

Open Write the equation of a line given the lope and a point on the line. in a new tab

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Line Given Two Points

Question: How do I write an equation ofa line when given two points on the line in slope-intercept form?

Answer: Find the slope of the line using the slope formula . Then use the point-slope (y − y₁ = m(x − x₁)) form of an equation of a line.

Example #4

Open Write the Equation of a Line Given Two Points on the Line in a new tab

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Writing a Linear Equation in Standard Form

Many times we are asked to give the equation of a line in Standard Form. Standard Form of a linear equation is: ax + by = c

Where a, b, and c are integers and a is positive.

For example: 5x + 4y = 20 is in standard form. a = 5, b = 4, and c = 20.

−3x − 5y = −8 is not in standard form, because a = −3 and a must be positive.

Changing from SLope-Intercept Form to Standard Form

To change an equation from slope-intercept form to standard form,

• the x and y terms must be removed ot the left side of the eqation
• the constand term must be on the right side of the equation
• all fractions muse be cleared
• the coefficient in front of x must be positive

ax + by = c

Example #5

Watch Change an Equation from Slope-Intercept Form to Standard Form.

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Example #6

Watch Write Equations of Parallel Lines

Open Write Equations of Parallel Lines in a new tab

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Example #7

Watch Write Equations of Perpendicular Lines

Open Write Equations of Perpendicular Lines in a new tab

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