The correct option is [tex]\boxed{\bf option\ (A)}[/tex].
Further explanation:
The linear equation of the line is [tex]y=mx+b[/tex] where [tex]m[/tex] is the slope of the line and [tex]b[/tex] is the [tex]y[/tex]-intercept of the line.
Suppose the line passes through the two pints [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex].
Therefore, the slope of the line is calculated as follows:
[tex]\boxed{m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}}[/tex]
Given:
The coordinates of the line are [tex](-1,8)[/tex] and [tex](2,-4)[/tex] as shown in the attached Figure 1 (attached in the end).
Calculation:
From the attached Figure 1 we can see that the line passes through the point [tex](-1,8)[/tex] and [tex](2,-4)[/tex].
Substitute [tex]8[/tex] for [tex]y_{2}[/tex], [tex]-1[/tex] for [tex]x_{2}[/tex], [tex]-4[/tex] for [tex]y_{1}[/tex] and [tex]2[/tex] for [tex]x_{1}[/tex] in the equation.
Use the formula of the slope of the line to obtain the value of [tex]m[/tex].
The value of [tex]m[/tex] is calculated as follows:
[tex]\begin{aligned}m&=\dfrac{8-(-4)}{-1-(2)}\\&=\dfrac{12}{-3}\\&=-4\end{aligned}[/tex]
Therefore, the slope of the line is [tex]\boxed{-4}[/tex].
This implies that the correct option is [tex]\boxed{\bf option\ (A)}[/tex].
Learn more:
1. Learn more about the representation of the graph https://brainly.com/question/2491745
2. Learn more about the graph of the quadratic function https://brainly.com/question/2334270
3. Learn more about graphed below of the function https://brainly.com/question/9590016
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Straight lines
Keywords: Linear equations, equation, line, slope, intercept, coordinate, solutions set, graph, curve, angle, parallel, perpendicular, straight line, pairs, point, ccordinate.
