Question

what is the slope of this line? simplify your answer completely. slope = $-\frac{?}{\square}$ slope: $\frac{\text{rise}}{\text{run}}$

Explanation:

Step1: Identify two points on the line

The line passes through \((0, 3)\) and \((3, 0)\) (we can also use other points like \((1, 2)\) and \((2, 1)\), but \((0, 3)\) and \((3, 0)\) are easy to identify from the graph).

Step2: Calculate the rise and run

Rise is the change in \(y\)-values: \(y_2 - y_1 = 0 - 3 = - 3\) (or we can think of "rise" as the vertical change, and since the line is decreasing, the rise can also be considered as negative when moving from left to right). Run is the change in \(x\)-values: \(x_2 - x_1 = 3 - 0 = 3\). But using the formula \(\text{slope}=\frac{\text{rise}}{\text{run}}\), if we take two points \((0, 3)\) and \((1, 2)\), rise is \(2 - 3=-1\), run is \(1 - 0 = 1\), but let's use the \(y\)-intercept point \((0, 3)\) and when \(y = 0\), \(x = 3\). Alternatively, using the slope formula \(\frac{y_2 - y_1}{x_2 - x_1}\), with \((x_1,y_1)=(0,3)\) and \((x_2,y_2)=(3,0)\), we get \(\frac{0 - 3}{3 - 0}=\frac{-3}{3}=- 1\). Wait, but the problem shows slope \(=-\frac{[?]}{[?]}\). Let's use the two points \((0, 3)\) and \((1, 2)\): rise is \(2 - 3=-1\), run is \(1 - 0 = 1\), but also, from \((0,3)\) to \((3,0)\), rise is \(0 - 3=-3\), run is \(3 - 0 = 3\), so \(\frac{-3}{3}=-1\), but simplifying \(\frac{-3}{3}\) gives \(-1\), but the form is \(-\frac{[?]}{[?]}\). Wait, maybe using the points \((0,3)\) and \((1,2)\): rise is \(2 - 3=-1\), run is \(1 - 0 = 1\), but if we consider the "rise" as the vertical change when moving from left to right, from \(x = 0\) to \(x = 1\), \(y\) goes from \(3\) to \(2\), so rise is \(-1\), run is \(1\), so slope is \(\frac{-1}{1}\), but the problem has slope \(=-\frac{[?]}{[?]}\). Wait, maybe the two points are \((0,3)\) and \((3,0)\), so rise is \(0 - 3=-3\), run is \(3 - 0 = 3\), so \(\frac{-3}{3}=-\frac{3}{3}\), but simplifying, but the problem wants the numerator and denominator before simplifying? No, the problem says "simplify your answer completely". Wait, maybe I made a mistake. Let's look at the graph again. The line crosses the \(y\)-axis at \(3\) (so \(y\)-intercept is \(3\)) and when[SSE Completed, Client Connection Error][SSE onError error]

Answer:

Step1: Identify two points on the line

The line passes through \((0, 3)\) and \((3, 0)\) (we can also use other points like \((1, 2)\) and \((2, 1)\), but \((0, 3)\) and \((3, 0)\) are easy to identify from the graph).

Step2: Calculate the rise and run

Rise is the change in \(y\)-values: \(y_2 - y_1 = 0 - 3 = - 3\) (or we can think of "rise" as the vertical change, and since the line is decreasing, the rise can also be considered as negative when moving from left to right). Run is the change in \(x\)-values: \(x_2 - x_1 = 3 - 0 = 3\). But using the formula \(\text{slope}=\frac{\text{rise}}{\text{run}}\), if we take two points \((0, 3)\) and \((1, 2)\), rise is \(2 - 3=-1\), run is \(1 - 0 = 1\), but let's use the \(y\)-intercept point \((0, 3)\) and when \(y = 0\), \(x = 3\). Alternatively, using the slope formula \(\frac{y_2 - y_1}{x_2 - x_1}\), with \((x_1,y_1)=(0,3)\) and \((x_2,y_2)=(3,0)\), we get \(\frac{0 - 3}{3 - 0}=\frac{-3}{3}=- 1\). Wait, but the problem shows slope \(=-\frac{[?]}{[?]}\). Let's use the two points \((0, 3)\) and \((1, 2)\): rise is \(2 - 3=-1\), run is \(1 - 0 = 1\), but also, from \((0,3)\) to \((3,0)\), rise is \(0 - 3=-3\), run is \(3 - 0 = 3\), so \(\frac{-3}{3}=-1\), but simplifying \(\frac{-3}{3}\) gives \(-1\), but the form is \(-\frac{[?]}{[?]}\). Wait, maybe using the points \((0,3)\) and \((1,2)\): rise is \(2 - 3=-1\), run is \(1 - 0 = 1\), but if we consider the "rise" as the vertical change when moving from left to right, from \(x = 0\) to \(x = 1\), \(y\) goes from \(3\) to \(2\), so rise is \(-1\), run is \(1\), so slope is \(\frac{-1}{1}\), but the problem has slope \(=-\frac{[?]}{[?]}\). Wait, maybe the two points are \((0,3)\) and \((3,0)\), so rise is \(0 - 3=-3\), run is \(3 - 0 = 3\), so \(\frac{-3}{3}=-\frac{3}{3}\), but simplifying, but the problem wants the numerator and denominator before simplifying? No, the problem says "simplify your answer completely". Wait, maybe I made a mistake. Let's look at the graph again. The line crosses the \(y\)-axis at \(3\) (so \(y\)-intercept is \(3\)) and when[SSE Completed, Client Connection Error][SSE onError error]