Identify the Linear Equation: Match the Graph's Function

Q: How do I know which points to choose from the graph?

Look for points where the line clearly passes through grid intersections. In this graph, (-3, 0) and (0, 5) are perfect because they're exactly on the grid lines with no guessing needed.

Q: What if I get a negative slope?

A negative slope means the line goes down from left to right. This line goes up from left to right, so we expect a positive slope like $ \frac{5}{3} $.

Q: How do I read the y-intercept from the graph?

The y-intercept is where the line crosses the y-axis (vertical axis). Look at x = 0 and see what y-value the line passes through. Here it's y = 5.

Q: Why is the slope a fraction instead of a whole number?

Slopes can be any real number! A fractional slope like $ \frac{5}{3} $ means for every 3 units right, the line goes up 5 units. This creates a moderate incline.

Q: What if none of the answer choices match my calculation?

Double-check your points first! Make sure they're exactly on grid intersections. Then recalculate the slope using the slope formula. Small errors in point selection cause big differences in the final 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 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?

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: $(-3, 0)$ and $(0, 5)$ .

Using these points, we calculate the slope $m$ :

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 $y = 5$ when $x = 0$ , so the y-intercept is 5.

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

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

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

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

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

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

3

Final Answer

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

Key Points to Remember

Essential concepts to master this topic

Point Selection: Choose two clear grid intersection points for accurate calculations
Slope Formula: Use $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5-0}{0-(-3)} = \frac{5}{3}$
Verification: Check that both identified points satisfy your final equation ✓

Common Mistakes

Avoid these frequent errors

Using unclear or estimated points from the graph
Don't pick points that aren't exactly on grid intersections = inaccurate slope calculations! Estimated coordinates lead to wrong fractions and incorrect equations. Always choose points where the line clearly passes through grid line intersections.

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 know which points to choose from the graph?

+

Look for points where the line clearly passes through grid intersections. In this graph, (-3, 0) and (0, 5) are perfect because they're exactly on the grid lines with no guessing needed.

What if I get a negative slope?

+

A negative slope means the line goes down from left to right. This line goes up from left to right, so we expect a positive slope like $\frac{5}{3}$ .

How do I read the y-intercept from the graph?

+

The y-intercept is where the line crosses the y-axis (vertical axis). Look at x = 0 and see what y-value the line passes through. Here it's y = 5.

Why is the slope a fraction instead of a whole number?

+

Slopes can be any real number! A fractional slope like $\frac{5}{3}$ means for every 3 units right, the line goes up 5 units. This creates a moderate incline.

What if none of the answer choices match my calculation?

+

Double-check your points first! Make sure they're exactly on grid intersections. Then recalculate the slope using the slope formula. Small errors in point selection cause big differences in the final equation.

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Identify the Linear Equation: Match the Graph's Function

Slope-Intercept Form with Point Identification

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