Question

what is the slope intercept equation

Explanation:

Step1: Identify two points on the line

Let's assume the grid has integer coordinates. From the graph, let's pick two points on the line (let's say) \((x_1, y_1)\) and \((x_2, y_2)\). Suppose the left point is \((-4, 2)\) and the right point is \((0, 1)\) (estimating from the grid).

Step2: Calculate the slope \(m\)

The formula for slope is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting the points: \(m=\frac{1 - 2}{0 - (-4)}=\frac{-1}{4}=-\frac{1}{4}\).

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

The y - intercept is the value of \(y\) when \(x = 0\). From the point \((0, 1)\), we see that \(b = 1\).

Step4: Write the slope - intercept equation

The slope - intercept form is \(y=mx + b\). Substituting \(m = -\frac{1}{4}\) and \(b = 1\), we get \(y=-\frac{1}{4}x + 1\).

Answer:

\(y = -\frac{1}{4}x + 1\) (Note: If the points estimated are different, the equation may vary slightly, but the process remains the same. The key is to correctly identify two points on the line, calculate the slope, find the y - intercept, and then write the equation in \(y=mx + b\) form.)