Equations of Lines (rearranging the furniture). There are three different forms of the equation of a line. Two are for “show”: slope-intercept equation.

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Presentation transcript:

Equations of Lines (rearranging the furniture)

There are three different forms of the equation of a line. Two are for “show”: slope-intercept equation of a line:y = mx + b standard equation of a line: Ax + By = C And one is a “workhorse”: point-slope equation of a line: y – y 1 = m( x – x 1 ) Three Forms of Linear Equations

The point-slope equation of a line: y – y 1 = m( x – x 1 ) is used to figure out the equation of a line when you are given a point and the slope. You never give your answer in point-slope form. Point-slope Equation of a Line

The slope-intercept equation of a line: y = mx + b is great for graphing. m is the slope of the line (0, b) is the y-intercept of the line You frequently are asked to give your answer in point-slope form. Slope-intercept Equation of a Line

The standard equation of a line: Ax + By = C is mainly for show. You frequently are asked to give your answer in standard form. Standard Equation of a Line

If they tell you that the slope is And the y-intercept is (0, – 5) The slope intercept equation is y = x – 5 Slope-intercept Form

The slope intercept equation is y = x – 5 To write that in standard form, first multiply each term by the LCD. 4y = 7x – 20 Then rearrange the furniture. – 7x + 4y = – 20 7x – 4y = 20 From slope-intercept to Standard Form Make x positive

What if they ask you to graph 7x – 4y = 20 Then rearrange the furniture – solve for y – 4y = 7x – 20 y = x – 5 Now you know the slope and the y-intercept and it’s easy to graph! From Standard to slope-intercept Form

Equations of lines Point-slope: never the form of an answer. Slope-intercept: Great for graphing. May be requested for an answer. Standard form: Frequently requested for answers.