Question

write an equation of the line below.

Explanation:

Step1: Identify two points

From the graph, we can see two points: \((0, 4)\) (the y - intercept) and \((-4, -6)\) (let's verify the coordinates visually: when \(x = 0\), \(y=4\); another point seems to be at \(x=- 4\), \(y = - 6\)).

Step2: Calculate the slope \(m\)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0,4)\) and \((x_2,y_2)=(-4,-6)\). Then \(m=\frac{-6 - 4}{-4-0}=\frac{-10}{-4}=\frac{5}{2}\).

Step3: Use slope - intercept form \(y = mx + b\)

The slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We know that \(m = \frac{5}{2}\) and from the point \((0,4)\), the y - intercept \(b = 4\). So the equation of the line is \(y=\frac{5}{2}x + 4\).

Answer:

\(y=\frac{5}{2}x + 4\)