To determine the slope of the line that passes through the points [tex]\((3, 4)\)[/tex] and [tex]\((5, 7)\)[/tex], we need to use the slope formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
where [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the two points.
Step 1: Identify the coordinates.
[tex]\[
(x_1, y_1) = (3, 4)
\][/tex]
[tex]\[
(x_2, y_2) = (5, 7)
\][/tex]
Step 2: Subtract the [tex]\(y\)[/tex]-coordinates to find the change in [tex]\(y\)[/tex] ([tex]\(\Delta y\)[/tex]).
[tex]\[
\Delta y = y_2 - y_1 = 7 - 4 = 3
\][/tex]
Step 3: Subtract the [tex]\(x\)[/tex]-coordinates to find the change in [tex]\(x\)[/tex] ([tex]\(\Delta x\)[/tex]).
[tex]\[
\Delta x = x_2 - x_1 = 5 - 3 = 2
\][/tex]
Step 4: Substitute the changes in [tex]\(y\)[/tex] and [tex]\(x\)[/tex] into the slope formula.
[tex]\[
m = \frac{\Delta y}{\Delta x} = \frac{3}{2}
\][/tex]
Thus, the slope of the line that passes through the points [tex]\((3, 4)\)[/tex] and [tex]\((5, 7)\)[/tex] is:
[tex]\[
m = \frac{3}{2}
\][/tex]
So, the correct and simplified form of the slope [tex]\(m\)[/tex] is:
[tex]\[
m = 1.5
\][/tex]
