Identify the Linear Equation: Match the Graph's Function

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the appropriate equation for the function in the table
00:03 We want to find the slope of the graph
00:06 Let's take 2 points on the graph
00:10 We'll use the formula to find the function graph's slope
00:14 Let's substitute appropriate values and solve to find the slope
00:20 This is the slope of the graph
00:23 Let's use the line equation
00:26 Let's substitute appropriate values and solve for B
00:45 This is the value of B (intersection point with Y axis)
00:49 Let's compose the line equation using the values we found
00:54 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

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

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2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Identify two clear points on the graph where the line passes through grid intersections.
  • Calculate the slope of the line using these points.
  • Determine the y-intercept by observing where the line crosses the y-axis.
  • Compare the calculated slope and intercept with the given equations to find the match.

Let's identify two points on the line. From the graph, we see the line passes through at least two points: (−3,0)(-3, 0) and (0,5)(0, 5).

Using these points, we calculate the slope m m :

m=y2−y1x2−x1=5−00−(−3)=53 m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 0}{0 - (-3)} = \frac{5}{3}

Next, observe that the y-intercept (where the line crosses the y-axis) corresponds to y=5 y = 5 when x=0 x = 0 , so the y-intercept is 5.

Now we can formulate the linear equation based on our calculations:

y=53x+5 y = \frac{5}{3} x + 5

After calculating the slope and intercept, we compare with the provided options:

  • Option 1: y=5x y = 5x – Slope and intercept do not match.
  • Option 2: y=−2x+4 y = -2x + 4 – Slope and intercept do not match.
  • Option 3: y=53x+5 y = \frac{5}{3}x + 5 – Both slope and intercept match exactly.
  • Option 4: y=8 y = 8 – Not a linear equation of this form.

Thus, the equation that corresponds to the function represented in the graph is:

y=53x+5 y = \frac{5}{3}x + 5

3

Final Answer

y=53x+5 y=\frac{5}{3}x+5

Practice Quiz

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Is the given graph a function?

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