Question

which of the following equations does the graph below represent? graph of a line on a coordinate plane with x-axis from -10 to 10 and y-axis from -10 to 10, intersecting y-axis at (0,5) and x-axis at (5,0) (approximate, based on grid)

Explanation:

Step1: Identify intercepts

The graph intersects the y - axis at (0, 5) (wait, looking again, the y - intercept: when x = 0, y is 5? Wait no, the grid: from the graph, when x = 0, y = 5? Wait no, let's check the x - intercept. The line crosses the x - axis at (5, 0)? Wait no, the x - axis crossing: looking at the graph, the line crosses the x - axis at (5, 0)? Wait the grid lines: each square is 1 unit. So when x = 0, y = 5? Wait no, the y - intercept: the point where x = 0. From the graph, the line passes through (0, 5)? Wait no, let's recalculate. Wait the slope: let's take two points. Let's take (0, 5) and (5, 0). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 5}{5 - 0}=\frac{- 5}{5}=- 1\). Wait, no, wait the x - intercept: when y = 0, x = 5? Wait the line in the graph: let's check the points. When x = 0, y = 5? Wait no, looking at the graph, the y - intercept is at (0, 5)? Wait the original graph: the y - axis has 0, 2, 4, 6... Wait no, the y - axis: the line crosses the y - axis at (0, 5)? Wait no, the grid: the y - axis, the line is at y = 5 when x = 0? Wait no, let's look again. The graph: the line passes through (0, 5) and (5, 0). So the slope is \(\frac{0 - 5}{5 - 0}=-1\). So the equation of the line in slope - intercept form \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. Here, \(m=-1\) and \(b = 5\), so the equation is \(y=-x + 5\). Wait, let's verify. When x = 0, y = 5 (correct, y - intercept). When y = 0, \(0=-x + 5\), so \(x = 5\) (correct, x - intercept).

Step2: Derive the equation

Using the slope - intercept form \(y=mx + b\). We found that the y - intercept \(b = 5\) (when x = 0, y = 5) and the slope \(m=\frac{0 - 5}{5 - 0}=-1\). So the equation of the line is \(y=-x + 5\), which can be rewritten as \(x + y=5\) or \(y=-x + 5\).

Answer:

The equation of the line is \(y=-x + 5\) (or equivalent forms like \(x + y = 5\))