Question

write the equation of this line in slope - intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through the points \((0, 5)\) (the y - intercept) and \((5, 5)\)? Wait, no, looking again, maybe \((0,5)\) and \((5,5)\) is not correct. Wait, let's check the coordinates. Wait, the line seems to pass through \((0,5)\) and maybe \((5,5)\)? No, that would be a horizontal line. Wait, the slope - intercept form is \(y = mx + b\), where \(b\) is the y - intercept and \(m\) is the slope. The y - intercept \(b\) is the value of \(y\) when \(x = 0\). From the graph, when \(x = 0\), \(y=5\)? Wait, no, looking at the grid, the line passes through \((0,5)\) and \((5,5)\)? Wait, no, if we take two points: let's say \((0,5)\) and \((5,5)\), the slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{5 - 5}{5 - 0}=0\). Wait, that would be a horizontal line \(y = 0x+5\) or \(y = 5\). Wait, maybe I misread the graph. Wait, the line is horizontal? Let's confirm. The slope - intercept form is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. If the line is horizontal, the slope \(m = 0\), and the y - intercept \(b\) is the y - coordinate of any point on the line. From the graph, the line crosses the y - axis at \(y = 5\), and since it's horizontal, the slope is 0. So the equation is \(y=0x + 5\) or \(y = 5\). Wait, maybe the two points are \((0,5)\) and \((5,5)\), so the change in \(y\) is \(5 - 5=0\), change in \(x\) is \(5 - 0 = 5\), so slope \(m=\frac{0}{5}=0\).

Step2: Write the equation in slope - intercept form

The slope - intercept form is \(y=mx + b\). We found that \(m = 0\) and \(b = 5\) (since when \(x = 0\), \(y = 5\)). So substituting into the formula, we get \(y=0x + 5\), which simplifies to \(y = 5\).

Answer:

\(y = 5\)