Take Note Key Concept: Slope-Intercept Form

The slope-intercept form of an equation of a line is y = m x + b , y equals m x plus b comma  where m is the slope of the line and (0, b) is the y-intercept.

Problem 2 Writing Linear Equations

What is an equation of each line?

1. m = 1 5 m equals , 1 fifth  and the y-intercept is ( 0 , − 3 ) open 0 comma negative 3 close

   y = m x + b Use the slope-intercept form . y = 1 5 x + ( − 3 ) Substitute  m = 1 5  and  b = − 3. y = 1 5 x − 3 Simplify . table with 3 rows and 3 columns , row1 column 1 , y , column 2 equals m x plus b , column 3 cap usetheslopeminusinterceptform . . , row2 column 1 , y , column 2 equals , 1 fifth , x plus . open , negative 3 , close , column 3 cap substitute . m equals , 1 fifth , and , b equals negative 3. , row3 column 1 , y , column 2 equals , 1 fifth , x minus 3 , column 3 cap simplify , . , end table

2. 

   Look at the line shown in the graph. The y-intercept is the point where the line crosses the y-axis, (0, 4), so b = 4 . b equals 4 .

   Use the second point (1, 1) to find the slope.

   m = y 2 − y 1 x 2 − x 1 = 1 − 4 1 − 0 = − 3 . m equals . fraction y sub 2 , minus , y sub 1 , over x sub 2 , minus , x sub 1 end fraction . equals . fraction 1 minus 4 , over 1 minus 0 end fraction . equals negative 3 . .

   So, y = − 3 x + 4 . y equals negative 3 x plus 4 .

✓ Got It?

2. What is an equation of each line?
   1. m = 6 , m equals 6 comma  y-intercept is (0, 5)
   2. 
   3. Reasoning Using the graph from part (b), do you get a different equation if you use ( − 6 , 0 ) negative 6 comma 0 close  and the y-intercept to find the slope of the line? Explain.