Question

1. slope (20 points)

the graph of a linear function is shown on the grid.
determine the values of m and b in the equation y = mx + b for the line.
slope (m):
y - intercept (b):
linear equation (slope - intercept form):
f(-6)=

Explanation:

Step1: Identify two points on the line

Let's take two clear - cut points on the line. For example, the points \((0, - 6)\) and \((-4,2)\).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using the points \((x_1,y_1)=(0, - 6)\) and \((x_2,y_2)=(-4,2)\), we have \(m=\frac{2-(-6)}{-4 - 0}=\frac{2 + 6}{-4}=\frac{8}{-4}=-2\).

Step3: Determine the y - intercept \(b\)

The y - intercept is the value of \(y\) when \(x = 0\). From the point \((0,-6)\), we can see that \(b=-6\).

Step4: Write the linear equation

The slope - intercept form of a line is \(y=mx + b\). Substituting \(m=-2\) and \(b = - 6\), we get \(y=-2x-6\).

Step5: Find \(f(-6)\)

Substitute \(x=-6\) into \(y=-2x - 6\). Then \(y=-2\times(-6)-6=12 - 6 = 6\).

Answer:

Slope (\(m\)): \(-2\)
Y - intercept (\(b\)): \(-6\)
Linear Equation (Slope - Intercept Form): \(y=-2x-6\)
\(f(-6)=6\)