Tips for success

Some problems require you to find the equations of lines.

Which matrix equation is represented by the graph below?

Tip 1

Use the equation y = mx + b, where m represents the slope and b is the y-intercept.

Tip 2

Rewrite the equations as matrices in standard form.

1. [ 1 − 1 2 − 1 ] [ x y ] = [ 1 − 2 ] . matrix with 2 rows and 2 columns , row1 column 1 , 1 , column 2 negative 1 , row2 column 1 , 2 , column 2 negative 1 , end matrix , matrix with 2 rows and 1 column , row1 column 1 , x , row2 column 1 , y , end matrix . equals . matrix with 2 rows and 1 column , row1 column 1 , 1 , row2 column 1 , negative 2 , end matrix
2. [ − 1 − 1 1 − 1 ] [ x y ] = [ 1 − 2 ] . matrix with 2 rows and 2 columns , row1 column 1 , negative 1 , column 2 negative 1 , row2 column 1 , 1 , column 2 negative 1 , end matrix , matrix with 2 rows and 1 column , row1 column 1 , x , row2 column 1 , y , end matrix . equals . matrix with 2 rows and 1 column , row1 column 1 , 1 , row2 column 1 , negative 2 , end matrix
3. [ − 1 − 1 2 − 1 ] [ x y ] = [ 1 − 2 ] . matrix with 2 rows and 2 columns , row1 column 1 , negative 1 , column 2 negative 1 , row2 column 1 , 2 , column 2 negative 1 , end matrix , matrix with 2 rows and 1 column , row1 column 1 , x , row2 column 1 , y , end matrix . equals . matrix with 2 rows and 1 column , row1 column 1 , 1 , row2 column 1 , negative 2 , end matrix
4. [ − 1 − 1 2 − 1 ] [ x y ] = [ 2 1 ] . matrix with 2 rows and 2 columns , row1 column 1 , negative 1 , column 2 negative 1 , row2 column 1 , 2 , column 2 negative 1 , end matrix , matrix with 2 rows and 1 column , row1 column 1 , x , row2 column 1 , y , end matrix . equals , matrix with 2 rows and 1 column , row1 column 1 , 2 , row2 column 1 , 1 , end matrix

Think It Through

The slope of line a is − 1 negative 1  and its y-intercept is ( 0 , − 1 ) . open 0 comma negative 1 close .

The equation of line a is y = − x − 1 . y equals negative x minus 1 .

As a matrix equation in standard form, the equation of line a is [ − 1 − 1 ] [ x y ] = [ 1 ] . . matrix with 1 row and 2 columns , row1 column 1 , negative 1 , column 2 negative 1 , end matrix , matrix with 2 rows and 1 column , row1 column 1 , x , row2 column 1 , y , end matrix . equals , left bracket 1 right bracket , .

The slope of line b is 2 and its y-intercept is (0, 2).

The equation of line b is y = 2 x + 2 . y equals 2 x plus 2 .

As a matrix equation in standard form, the equation of line b is [ 2 − 1 ] [ x y ] = [ − 2 ] . . matrix with 1 row and 2 columns , row1 column 1 , 2 , column 2 negative 1 , end matrix , matrix with 2 rows and 1 column , row1 column 1 , x , row2 column 1 , y , end matrix . equals . left bracket , negative 2 , right bracket . .

The correct answer is C.