Question

write the equation of the line graphed below in simplest form.

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((0, 10)\) (the y - intercept) and let's find another point. Looking at the grid, when \(x = 2\), \(y = 9\)? Wait, no, maybe I misread. Wait, actually, let's check the slope. Wait, the y - intercept is \(b = 10\)? Wait, no, maybe the line is decreasing? Wait, no, maybe I made a mistake. Wait, let's look again. Wait, the graph: the y - axis has 10 at the top, and the line—wait, maybe the two points are \((0, 10)\) and \((2, 9)\)? No, that would be a negative slope. Wait, or maybe \((0, 10)\) and \((5, 0)\)? Wait, no, the x - axis crosses at some point. Wait, maybe the line is \(y=-\frac{2}{1}x + 10\)? Wait, no, let's do it properly.

Wait, let's find two clear points. Let's say the line passes through \((0, 10)\) (y - intercept) and \((5, 0)\) (x - intercept). Let's verify. The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 10}{5 - 0}=\frac{- 10}{5}=- 2\). So the slope \(m=-2\) and \(b = 10\). So the equation in slope - intercept form is \(y=-2x + 10\). To write it in standard form (Ax+By = C), we can rearrange: \(2x+y=10\). Wait, but let's check with another point. If \(x = 1\), then \(y=-2(1)+10 = 8\). Does the line pass through \((1, 8)\)? From the graph, that seems reasonable.

Step2: Write the equation

We know the slope - intercept form is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We found \(m=-2\) and \(b = 10\), so \(y=-2x + 10\). To write it in simplest form (standard form or slope - intercept, but usually for a line, slope - intercept or standard). Let's confirm the slope. The change in y over change in x: from \((0, 10)\) to \((5, 0)\), \(y\) changes by \(- 10\), \(x\) changes by \(5\), so slope \(m=\frac{-10}{5}=-2\). So the equation is \(y=-2x + 10\), which can be written as \(2x + y=10\) (standard form) or \(y=-2x + 10\) (slope - intercept).

Answer:

\(y=-2x + 10\) (or \(2x + y = 10\))