The slope of line passing through the points [tex]\left( { - 1,3} \right)[/tex] and [tex]\left( {4, - 7} \right)[/tex] is [tex]\boxed{ - 2}[/tex]. Option A is correct.
Further explanation:
The linear equation with slope m and intercept c is given as follows.
[tex]\boxed{y = mx + c}[/tex]
The formula for slope of line with points [tex]\left( {{x_1},{y_1}} \right)[/tex] and [tex]\left( {{x_2},{y_2}} \right)[/tex] can be expressed as,
[tex]\boxed{m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}[/tex]
Given:
The passes through point is [tex]\left( { - 2, 2} \right).[/tex]
Explanation:
The passes through points are [tex]\left( { - 1, 3} \right)[/tex] and [tex]\left( {4, - 7} \right).[/tex]
The slope of the line can be obtained as follows,
[tex]\begin{aligned}m &= \frac{{ - 7 - 3}}{{4 - \left( { - 1} \right)}}\\&= \frac{{ - 10}}{{4 + 1}}\\&= \frac{{ - 10}}{5}\\&=- 2\\\end{aligned}[/tex]
The slope of line passing through the points [tex]\left( { - 1,3} \right)[/tex] and [tex]\left( {4, - 7} \right)[/tex] is [tex]\boxed{ - 2}.[/tex] Option A is correct.
Option B is not correct.
Option C is not correct.
Option D is not correct.
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Linear equation
Keywords: numbers, slope, passes (-1,3), (4,-7), slope intercept, inequality, equation, linear inequality, y-intercept, graph, representation, origin, parallel.
