The correct option is \(\boxed{\bf option\ (A)}\).
Further explanation:
The linear equation of the line is \(y=mx+b\) where \(m\) is the slope of the line and \(b\) is the \(y\)-intercept of the line.
Suppose the line passes through the two pints \((x_{1},y_{1})\) and \((x_{2},y_{2})\).
Therefore, the slope of the line is calculated as follows:
\(\boxed{m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}}\)
Given:
The coordinates of the line are \((-1,8)\) and \((2,-4)\) 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 \((-1,8)\) and \((2,-4)\).
Substitute \(8\) for \(y_{2}\), \(-1\) for \(x_{2}\), \(-4\) for \(y_{1}\) and \(2\) for \(x_{1}\) in the equation.
Use the formula of the slope of the line to obtain the value of \(m\).
The value of \(m\) is calculated as follows:
\(\begin{aligned}m&=\dfrac{8-(-4)}{-1-(2)}\\&=\dfrac{12}{-3}\\&=-4\end{aligned}\)
Therefore, the slope of the line is \(\boxed{-4}\).
This implies that the correct option is \(\boxed{\bf option\ (A)}\).
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.
