To find the slope of a line containing two points, we can use the slope formula:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
where [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the two points. In this case, the points given are [tex]\((-3, 2)\)[/tex] and [tex]\((7, -1)\)[/tex].
1. Identify the coordinates:
- Point 1: [tex]\( (x_1, y_1) = (-3, 2) \)[/tex]
- Point 2: [tex]\( (x_2, y_2) = (7, -1) \)[/tex]
2. Substitute these coordinates into the slope formula:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
3. Calculate the numerator (the difference in the y-coordinates):
[tex]\[
y_2 - y_1 = -1 - 2 = -3
\][/tex]
4. Calculate the denominator (the difference in the x-coordinates):
[tex]\[
x_2 - x_1 = 7 - (-3) = 7 + 3 = 10
\][/tex]
5. Substitute the calculated numerator and denominator into the slope formula:
[tex]\[
\text{slope} = \frac{-3}{10}
\][/tex]
Thus, the expression used to find the slope of the line containing the points [tex]\((-3, 2)\)[/tex] and [tex]\((7, -1)\)[/tex] is:
[tex]\[ \frac{-3}{10} \][/tex]
So, the slope of the line is [tex]\( -0.3 \)[/tex]. This represents a line that decreases [tex]\(0.3\)[/tex] units in y for each unit it increases in x.
