Note: this answer assumes that the equation of the line must be in slope-intercept form.
Answer:
[tex]y= -3x + 5[/tex]
Explanation:
When you need to write an equation and know its slope and a point it intersects, you can use the point slope formula [tex]y-y_1 = m (x-x_1)[/tex] first. In order to write an equation using this formula, the [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex] must be substituted in for real values.
The [tex]m[/tex] represents the slope, so write the slope of this equation, -3, in its place. The [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line intersects. We know that the line must intersect the point (2, -1). Write 2 in the place of
[tex]y-(-1) = -3(x-(2))[/tex]
[tex]y+1 = -3(x-2)[/tex]
Now, to put it in slope-intercept or [tex]y = mx + b[/tex] form, just expand the right side and isolate [tex]y[/tex]:
[tex]y+1 = -3(x-2)\\y + 1 = -3x + 6 \\y = -3x + 5[/tex]
Therefore, [tex]y= -3x + 5[/tex] is the answer.
