Question

what is the equation for the line that passes through the points (4,2) and (0,6)? y = -x + 6; y = -x - 6; y = x + 6; y = -2x + 2

Explanation:

Step1: Find the slope (m)

The slope formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Given points \((4,2)\) and \((0,6)\), here \(x_1 = 4\), \(y_1 = 2\), \(x_2 = 0\), \(y_2 = 6\). So \(m=\frac{6 - 2}{0 - 4}=\frac{4}{-4}=-1\).

Step2: Find the y - intercept (b)

The point - slope form of a line is \(y=mx + b\). We know that the line passes through the point \((0,6)\), which is the y - intercept (when \(x = 0\), \(y=b\)). So \(b = 6\).

Step3: Write the equation of the line

Using the slope - intercept form \(y=mx + b\) with \(m=-1\) and \(b = 6\), we get \(y=-x + 6\).

Answer:

\(y=-x + 6\) (the green option: \(y=-x + 6\))