Question

Identify the slope and the y-intercept

Slope(m) =


y-intercept(b)=

3,9
4,7

Answer 1

To find the slope (m) and the y-intercept (b) of the line that passes through the points (3, 9) and (4, 7), we can follow these steps:

1. **Calculate the slope (m)** using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
where \((x_1, y_1)\) = (3, 9) and \((x_2, y_2)\) = (4, 7).

Plugging in the values:
\[
m = \frac{7 - 9}{4 - 3} = \frac{-2}{1} = -2
\]

2. **Use the slope-intercept form of a linear equation** to find the y-intercept (b). The slope-intercept form is:
\[
y = mx + b
\]
We can use one of the points to solve for \(b\). Let's use the point (3, 9).

Plugging in the values:
\[
9 = -2(3) + b
\]
\[
9 = -6 + b
\]
\[
b = 9 + 6 = 15
\]

So we have:

- Slope (m) = -2
- y-intercept (b) = 15

Final answers:
- Slope (m) = -2
- y-intercept (b) = 15