To find the slope of a line parallel to the line passing through points [tex]\(A(1, -3)\)[/tex] and [tex]\(B(-4, 7)\)[/tex], we first need to calculate the slope of line [tex]\(AB\)[/tex].
The formula for the slope [tex]\(m\)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
For points [tex]\(A(1, -3)\)[/tex] and [tex]\(B(-4, 7)\)[/tex]:
1. [tex]\( (x_1, y_1) = (1, -3) \)[/tex]
2. [tex]\( (x_2, y_2) = (-4, 7) \)[/tex]
Plugging these coordinates into the slope formula:
[tex]\[
m = \frac{7 - (-3)}{-4 - 1}
\][/tex]
Simplify the numerator and the denominator:
[tex]\[
m = \frac{7 + 3}{-4 - 1} = \frac{10}{-5} = -2
\][/tex]
Thus, the slope of the line passing through points [tex]\(A\)[/tex] and [tex]\(B\)[/tex] is [tex]\(-2\)[/tex].
A line that is parallel to line [tex]\(AB\)[/tex] will have the same slope. Therefore, the slope of a line parallel to line [tex]\(AB\)[/tex] is also [tex]\(-2\)[/tex].
The answer is:
[tex]\[
m = -2
\][/tex]
