Identify the Matching Equation for the Linear Graph

Video Solution

Solution Steps

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

00:04 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 graph's slope

00:13 We'll substitute appropriate values according to the given data and solve for the slope

00:18 This is the slope of the graph

00:22 We'll use the linear equation

00:26 We'll substitute appropriate values and solve for B

00:37 This is the value of B (intersection point with Y-axis)

00:41 We'll construct the linear equation using the values we found

00:46 And this is the solution to the question

Step-by-Step Solution

To solve the problem, follow these steps:

Now, let's work through each step:

Step 1: Upon examining the graph, let's assume it passes through the points $(0, 4)$ and $(3, 0)$ .

Step 2: Calculate the slope $m$ using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ :
$m = \frac{0 - 4}{3 - 0} = \frac{-4}{3}$ .

Step 3: Use the y-intercept point, which is already identified as $(0, 4)$ . Hence, $b = 4$ .

Thus, the equation of the line is $y = -\frac{4}{3}x + 4$ .

Step 4: Compare this to the choices: The correct choice is $y = -\frac{4}{3}x + 4$ , which matches the equation we derived.

Therefore, the solution to the problem is $y = -\frac{4}{3}x + 4$ .