Linear Function: Match the Graph to its Correct Equation

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

Choose points where the line crosses grid intersections clearly! Points like (0, -2) and (-2, 0) are perfect because they have integer coordinates and are easy to read accurately.

Q: What if I get a positive slope but the line goes down?

That means you mixed up your coordinates! A line that goes down from left to right always has a negative slope. Double-check your $ y_2 - y_1 $ and $ x_2 - x_1 $ calculations.

Q: How do I find the y-intercept from the equation?

The y-intercept is the constant term in $ y = mx + b $! In $ y = -x - 2 $, the y-intercept is -2, which means the line crosses the y-axis at (0, -2).

Q: Can I use any two points on the line?

Yes! Any two points will give you the same slope. But choose points that are far apart and have clear integer coordinates to avoid calculation errors.

Q: What does the negative slope tell me about the line?

A negative slope means the line is decreasing - as x increases, y decreases. The steeper the negative slope, the faster the line falls from left to right.

Linear Functions with Slope-Intercept Identification

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 graph

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

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

00:11 We'll use the formula to find the function's graph slope

00:15 We'll substitute appropriate values according to the given data and solve to find the slope

00:21 This is the slope of the graph

00:26 We'll use the linear equation

00:30 We'll substitute appropriate values and solve to find B

00:41 This is the value of B (intersection point with Y-axis)

00:46 We'll construct the linear equation using the values we found

00:49 And this is the solution to the question

Step-by-step written solution

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Understand the problem

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

Step-by-step solution

Let's use the below formula in order to find the slope:

$m=\frac{y_2-y_1}{x_2-x_1}$

We begin by inserting the known data from the graph into the formula:

$(0,-2),(-2,0)$

$m=\frac{-2-0}{0-(-2)}=$

$\frac{-2}{0+2}=$

$\frac{-2}{2}=-1$

We then substitute the point and slope into the line equation:

$y=mx+b$

$0=-1\times(-2)+b$

$0=2+b$

Lastly we combine the like terms:

$0+(-2)=b$

$-2=b$

Therefore, the equation will be:

$y=-x-2$

Final Answer

$y=-x-2$

Key Points to Remember

Essential concepts to master this topic

Slope Formula: Use two clear points to calculate $m = \frac{y_2 - y_1}{x_2 - x_1}$
Technique: Points (0, -2) and (-2, 0) give slope $m = \frac{-2}{2} = -1$
Check: Verify y-intercept by substituting x = 0 into final equation ✓

Common Mistakes

Avoid these frequent errors

Mixing up coordinate order when calculating slope
Don't switch x and y values when using (0, -2) and (-2, 0) = wrong slope sign! This reverses the line's direction completely. Always keep coordinates consistent: subtract y-values over x-values in the same order.

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 crosses grid intersections clearly! Points like (0, -2) and (-2, 0) are perfect because they have integer coordinates and are easy to read accurately.

What if I get a positive slope but the line goes down?

That means you mixed up your coordinates! A line that goes down from left to right always has a negative slope. Double-check your $y_2 - y_1$ and $x_2 - x_1$ calculations.

How do I find the y-intercept from the equation?

The y-intercept is the constant term in $y = mx + b$ ! In $y = -x - 2$ , the y-intercept is -2, which means the line crosses the y-axis at (0, -2).

Can I use any two points on the line?

Yes! Any two points will give you the same slope. But choose points that are far apart and have clear integer coordinates to avoid calculation errors.

What does the negative slope tell me about the line?

A negative slope means the line is decreasing - as x increases, y decreases. The steeper the negative slope, the faster the line falls from left to right.

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