Question

find the equation of a line with a slope of -4 that goes throguh point (2,3)

Answer 1

To find the equation of a line with a given slope and a point it passes through, you can use the point-slope form of the equation of a line, which is:

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

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

In this case, the slope \(m = -4\) and the point \((x_1, y_1) = (2, 3)\).

Substituting these values into the equation:

\[
y - 3 = -4(x - 2)
\]

Now, simplify the equation:

\[
y - 3 = -4x + 8
\]

\[
y = -4x + 8 + 3
\]

\[
y = -4x + 11
\]

So the equation of the line is:

\[
y = -4x + 11
\]