Question

What is the slope and equation of a line through the points (0, 9) and (3, 0)?
m = StartFraction 9 minus 0 Over 0 minus 3 EndFraction; y = –3x + 9
m = StartFraction 9 minus 0 Over 0 minus 3 EndFraction; y = –3x + 3
m = StartFraction 3 minus 0 Over 0 minus 9 EndFraction; y = negative one-third x + 9
m = StartFraction 3 minus 0 Over 0 minus 9 EndFraction; y = negative one-third x + 3

Answer 1

To find the slope (m) of the line passing through the points \((0, 9)\) and \((3, 0)\), we can use the slope formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Here, \((x_1, y_1) = (0, 9)\) and \((x_2, y_2) = (3, 0)\). Plugging in these values:

\[
m = \frac{0 - 9}{3 - 0} = \frac{-9}{3} = -3
\]

Next, we can use the point-slope form of the line equation, which is \(y - y_1 = m(x - x_1)\). Using the point \((0, 9)\):

\[
y - 9 = -3(x - 0)
\]

Simplifying this, we get:

\[
y - 9 = -3x
\]
\[
y = -3x + 9
\]

Thus, the slope is \(-3\) and the equation of the line is \(y = -3x + 9\).

So the correct answer is:
**m = StartFraction 9 minus 0 Over 0 minus 3 EndFraction; y = –3x + 9.**