Identify the Matching Equation for the Linear Graph

Q: How do I pick the best points from the graph?

Choose points where the line clearly passes through grid intersections. Avoid points between grid lines as they're harder to read accurately. Points like $(0, 4)$ and $(3, 0)$ are perfect!

Q: How can I tell which point is the y-intercept?

The y-intercept is where the line crosses the y-axis, so the x-coordinate is always 0. Look for the point $(0, b)$ where b is your y-intercept value.

Q: Do I always need to use the slope-intercept form?

For this type of problem, yes! The slope-intercept form $ y = mx + b $ makes it easy to identify slope and y-intercept directly from the equation.

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 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 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?

2

Step-by-step solution

To solve the problem, follow these steps:

Step 1: Identify two clear points on the line from the graph.
Step 2: Determine the slope using these two points.
Step 3: Find the y-intercept using the slope-intercept form of the equation.
Step 4: Compare the derived equation to the provided choices.

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 $y = -\frac{4}{3}x + 4$ .

3

Final Answer

$y=-\frac{4}{3}x+4$

Key Points to Remember

Essential concepts to master this topic

Graph Reading: Identify two clear points on the line accurately
Slope Formula: Use $m = \frac{y_2 - y_1}{x_2 - x_1}$ like $m = \frac{0 - 4}{3 - 0} = -\frac{4}{3}$
Verification: Check that chosen points satisfy your equation: $y = -\frac{4}{3}(0) + 4 = 4$ ✓

Common Mistakes

Avoid these frequent errors

Reading graph coordinates incorrectly
Don't confuse x and y coordinates or misread grid values = wrong slope calculation! A point at (3, 0) read as (0, 3) gives slope 3/4 instead of -4/3. Always double-check coordinates by tracing from axes to intersection points carefully.

Practice Quiz

Test your knowledge with interactive questions

Determine whether the following table represents a constant function:

FAQ

Everything you need to know about this question

How do I pick the best points from the graph?

+

Choose points where the line clearly passes through grid intersections. Avoid points between grid lines as they're harder to read accurately. Points like $(0, 4)$ and $(3, 0)$ are perfect!

What if I get a different slope than the answer choices?

+

Double-check your coordinate reading first! Then verify your slope calculation. Remember: negative slope means the line goes down from left to right, positive slope goes up.

How can I tell which point is the y-intercept?

+

The y-intercept is where the line crosses the y-axis, so the x-coordinate is always 0. Look for the point $(0, b)$ where b is your y-intercept value.

Do I always need to use the slope-intercept form?

+

For this type of problem, yes! The slope-intercept form $y = mx + b$ makes it easy to identify slope and y-intercept directly from the equation.

What if my calculated equation doesn't match any answer choice exactly?

+

Check if your fraction can be simplified or if you made a sign error. Also verify that your slope calculation used the correct order: $\frac{\text{change in y}}{\text{change in x}}$ .

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Functions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

Identify the Matching Equation for the Linear Graph

Linear Equations with Graphical Analysis

❤️ Continue Your Math Journey!