Question

passes through point (2,-1) and has a slope of -3?
a. y=-3x-1
b. y=-3x-5
c. y=-3x+1
d. y=-3x+5

Answer 1

To find the equation of a line that passes through the point (2, -1) with a slope of -3, we can use the point-slope form of the equation of a line, which is given by:

\[
y - y_1 = m(x - x_1)
\]

where \( (x_1, y_1) \) is the point the line passes through and \( m \) is the slope.

Substituting the given point (2, -1) and the slope -3 into the equation:

\[
y - (-1) = -3(x - 2)
\]

This simplifies to:

\[
y + 1 = -3(x - 2)
\]

Distributing the -3:

\[
y + 1 = -3x + 6
\]

Now, subtract 1 from both sides to isolate \( y \):

\[
y = -3x + 5
\]

So the equation of the line is:

\[
y = -3x + 5
\]

Thus, the correct answer is **d. y = -3x + 5.**