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Unit 6.1
Write Linear Equations in Slope-Intercept Form


                     TABLE

   GRAPH                             EQUATION

                      RULE
        •   How can we recognize a linear equation?
        •   How do we know our rule is correct?
        •   What does the representation tell us?
        •   What are the connections between representations?
Example 1     Use slope and y-intercept to write an equation

Write an equation of the line with a slope of – 2 and a
y-intercept of 5.

        y = mx + b         Write slope-intercept form.


        y = – 2x + 5       Substitute – 2 for m and 5 for b.
Example 2      Write an equation of a line from a graph

Write an equation of the line shown.

SOLUTION
                             –2    2
The slope of the line is m =    = – .
                             5     5
The line crosses the y-axis at (0, 3).
So, the y-intercept is b = 3 .

     y = mx + b          Write slope-intercept form.

          2                          2
     y = – x + 3         Substitute – for m and 3 for b.
          5                          5
Guided Practice    for Examples 1 and 2

1. Write an equation of the line with a slope of 8 and a
   y-intercept of – 7.

ANSWER       y = 8x – 7
Guided Practice   for Examples 1 and 2

Write an equation of the line shown.

                                                 3
2.                            ANSWER          y = x –2
                                                 2




3.                            ANSWER          y = – 3x + 4
Example 3    Write an equation of a line given two points

Write an equation of the line shown.




STEP 1 Calculate the slope.
             y2 – y1  –1 – (–5)   4
        m =         =           =
            x2 – x1    3 – 0      3
Example 3      Write an equation of a line given two points

STEP 2 Write an equation of the line. The line crosses
       the y-axis at (0, – 5 ). So, the y-intercept is b = – 5.
         y = mx + b             Write slope-intercept form.
            4                                4
         y = x – 5              Substitute     for m and – 5 for b.
            3                                3
Example 4      Find the slope or y-intercept given a point

Find the value of m or b if the given line passes through
the given point.
a. y = mx + 1; ( 3, – 2)       b. y = 2x + b; (– 1, – 4)

SOLUTION
a. Substitute the coordinates of the given point into
   the equation and solve for m.
     y = mx + 1                Write original equation.

   –2 = m ( 3) + 1             Substitute 3 for x and – 2 for y.

   –3 = 3m                     Subtract 1 from each side.

   –1 = m                      Divide each side by 3.
Example 4     Find the slope or y-intercept given a point

b. Substitute the coordinates of the given point into
   the equation and solve for b.
    y = 2x + b                Write original equation.

   –4 = 2(–1) + b             Substitute –1 for x and – 4 for y.

   –4 = –2 + b                Multiply.

   –2 = b                     Add 2 to each side.

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Unit 6.1

  • 1. Unit 6.1 Write Linear Equations in Slope-Intercept Form TABLE GRAPH EQUATION RULE • How can we recognize a linear equation? • How do we know our rule is correct? • What does the representation tell us? • What are the connections between representations?
  • 2. Example 1 Use slope and y-intercept to write an equation Write an equation of the line with a slope of – 2 and a y-intercept of 5. y = mx + b Write slope-intercept form. y = – 2x + 5 Substitute – 2 for m and 5 for b.
  • 3. Example 2 Write an equation of a line from a graph Write an equation of the line shown. SOLUTION –2 2 The slope of the line is m = = – . 5 5 The line crosses the y-axis at (0, 3). So, the y-intercept is b = 3 . y = mx + b Write slope-intercept form. 2 2 y = – x + 3 Substitute – for m and 3 for b. 5 5
  • 4. Guided Practice for Examples 1 and 2 1. Write an equation of the line with a slope of 8 and a y-intercept of – 7. ANSWER y = 8x – 7
  • 5. Guided Practice for Examples 1 and 2 Write an equation of the line shown. 3 2. ANSWER y = x –2 2 3. ANSWER y = – 3x + 4
  • 6. Example 3 Write an equation of a line given two points Write an equation of the line shown. STEP 1 Calculate the slope. y2 – y1 –1 – (–5) 4 m = = = x2 – x1 3 – 0 3
  • 7. Example 3 Write an equation of a line given two points STEP 2 Write an equation of the line. The line crosses the y-axis at (0, – 5 ). So, the y-intercept is b = – 5. y = mx + b Write slope-intercept form. 4 4 y = x – 5 Substitute for m and – 5 for b. 3 3
  • 8. Example 4 Find the slope or y-intercept given a point Find the value of m or b if the given line passes through the given point. a. y = mx + 1; ( 3, – 2) b. y = 2x + b; (– 1, – 4) SOLUTION a. Substitute the coordinates of the given point into the equation and solve for m. y = mx + 1 Write original equation. –2 = m ( 3) + 1 Substitute 3 for x and – 2 for y. –3 = 3m Subtract 1 from each side. –1 = m Divide each side by 3.
  • 9. Example 4 Find the slope or y-intercept given a point b. Substitute the coordinates of the given point into the equation and solve for b. y = 2x + b Write original equation. –4 = 2(–1) + b Substitute –1 for x and – 4 for y. –4 = –2 + b Multiply. –2 = b Add 2 to each side.