Identify the Linear Equation with a Slope of -1 from the Graph

Question

Which of the following equations corresponds to the function represented in the graph?

00:00 Find the appropriate equation for the function in the table

00:03 We want to find the slope of the graph

00:07 Let's take 2 points on the graph

00:10 We'll use the formula to find the function's graph slope

00:14 We'll substitute appropriate values according to the given data and solve to find the slope

00:24 This is the slope of the graph

00:29 We'll use the linear equation

00:32 We'll substitute appropriate values and solve to find B

00:44 This is the value of B (Y-axis intercept)

00:50 We'll construct the linear equation using the values we found

00:54 And this is the solution to the question

To match the graph to the correct equation, we will analyze the slope and y-intercept:

Step 1: Identify y-intercept.
From the graph, observe that the line crosses the y-axis at $y = 4$ . Therefore, the y-intercept $b = 4$ .
Step 2: Calculate slope.
Identify two points on the graph line, such as $(0, 4)$ and $(5, 0)$ . Calculate slope using $m = \frac{\Delta y}{\Delta x}$ :
$m = \frac{0 - 4}{5 - 0} = \frac{-4}{5}$ .
**Step 3: Match to equations**.
Now we have $m = -\frac{4}{5}$ and $b = 4$ , so the equation should be $y = -\frac{4}{5}x + 4$ .

After comparing with the choices, we see that choice $(2)$ $y = -\frac{4}{5}x + 4$ correctly matches the information derived from the graph.

Therefore, the equation that corresponds to the graph is $y = -\frac{4}{5}x + 4$ .

$y=-\frac{4}{5}x+4$