If the slope of a line is -1 and the y-intercept is 3, what is the equation of the line?

The equation of a line is commonly represented in the slope-intercept form, which is given by the formula ( y = mx + b ), where ( m ) is the slope of the line and ( b ) is the y-intercept.

In this case, the slope of the line is provided as ( -1 ), and the y-intercept is given as ( 3 ). Substituting these values into the equation yields:

[

y = -1 \cdot x + 3

]

or simply,

[

y = -x + 3.

]

This equation indicates that for every unit increase in ( x ), ( y ) decreases by 1 unit (reflecting the negative slope), and when ( x = 0 ), ( y ) equals ( 3 ) (the y-intercept).

Thus, the correct expression for the line with the specified slope and intercept is ( y = -x + 3 ). This reaffirms why the choice accurately describes the line in question.