Question

Identify the slope and the y-intercept
the first dot is (3, 9), the second is (4, 7)
Slope(m) =


y-intercept(b)=

Answer 1

To find the slope (m) of the line that passes through the two points \((3, 9)\) and \((4, 7)\), you can use the formula for slope:

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

Assigning the coordinates from the points:

- \((x_1, y_1) = (3, 9)\)
- \((x_2, y_2) = (4, 7)\)

Now substitute the values into the formula:

\[
m = \frac{7 - 9}{4 - 3} = \frac{-2}{1} = -2
\]

So, the slope \(m\) is \(-2\).

Next, to find the y-intercept (b), we can use the slope-intercept form of the equation of a line:

\[
y = mx + b
\]

Using one of the points, for example, \((3, 9)\) and the slope \(-2\), we can substitute these values into the equation to solve for \(b\):

\[
9 = -2(3) + b
\]
\[
9 = -6 + b
\]
\[
b = 9 + 6 = 15
\]

Thus, the y-intercept \(b\) is \(15\).

In summary:

- Slope \(m = -2\)
- Y-intercept \(b = 15\)