Writing Linear Equations in Slope-Intercept Form

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Writing Linear Equations in Slope-Intercept Form
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Quick Review

• An equation of a line can be written in
  slope-intercept form
• y mx b
• where m is the slope and b is the y-intercept.
• The y-intercept is where a line crosses the
  y-axis.

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Writing an Equation of a Line

• Suppose the slope of a line is 5 and the
  y-intercept is 2. How would this you write the
  equation of this line in slope-intercept form?
• First write the slope-intercept form.
• y mx b
• Now substitute 5 for m and 2 for b.
• y 5x 2

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Write the Equation of a Line from a Graph

• Where does the line cross the y-axis?
• At the point (0, -4)
• The y-intercept is -4.
• What is the slope of the line?
• The graph also crosses the x-axis at (2, 0).
• We can use the slope formula to find our slope.
• m -4 0 -4 2
• 0 2 -2
• We know our slope is 2 and our y-intercept is -4,
  what is the equation of our line?

y mx b y 2x (-4) y 2x -4
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Lets try an example!

• Write the equation of a line with a slope of -2
  and a y-intercept of 6.
• y mx b
• y -2x 6

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Using a graph

• Where does the line cross the y-axis?
• At the point (0, 2)
• So the y-intercept b is 2.
• The line also passes through the point (3, 0).
• We can use these points to find the slope of the
  line. How? What formula do we use?
• Using the slope formula, we find that the slope m
  is -2/3.
• Write the equation of the line.
• y mx b
• y (-2/3)x 2

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If we are given the Slope and a Point

• Step 1
• First find the y-intercept. Substitute the slope
  m and the coordinates of the given point (x, y)
  into the slope-intercept form, y mx b. Then
  solve for the y-intercept b.
• Step 2
• Then write the equation of the line. Substitute
  the slope m and the y-intercept b into the
  slope-intercept form, y mx b.

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If We Are Given the Slope and a Point

• Suppose we have a slope of -3 and it passes
  through the point (1, 2).
• We first need to find the y-intercept. We can do
  this by substituting our information into
  slope-intercept form and solving for b.
• y mx b
• 2 -3(1) b
• 2 -3 b Add 3 to both sides.
• 5 b Now we know that the y-intercept is 5.
• y mx b
• y -3x 5

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Try This!

• Suppose we have a line with a slope of -1 and
  passes through the point (3, 4).
• y mx b
• 4 (-1)3 b
• 4 -3 b
• 7 b
• y mx b
• y (-1)x 7
• y -x 7