Identify the Linear Equation with a Slope of -1 from the Graph

Q: How do I know which direction is positive for slope?

Moving left to right: if the line goes up, slope is positive; if it goes down, slope is negative. In this graph, the line falls from left to right, so the slope is negative.

Q: What if I can't see exact points on the grid?

Look for points where the line passes through grid intersections. In this case, (0,4) and (5,0) are clear intersection points that make calculations easier.

Q: Why is the slope -4/5 and not -5/4?

Slope is always $ \frac{\text{rise}}{\text{run}} $. From (0,4) to (5,0): we go down 4 units (rise = -4) and right 5 units (run = +5), giving us $ \frac{-4}{5} $.

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

The y-intercept is where the line crosses the y-axis (when x = 0). Look at the graph and see what y-value the line passes through on the vertical axis.

Q: Can I use any two points to find the slope?

Yes! Any two points on the line will give you the same slope. Choose points that are easy to read from the graph, preferably at grid intersections.

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

A negative slope means the line is decreasing - as x-values increase, y-values decrease. The line slants downward from left to right.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's find the right equation for the function shown in the table.

00:10 First, we need to determine the slope of the graph.

00:14 To do this, we'll pick two points on the graph.

00:18 Next, use the slope formula to calculate the slope.

00:22 Substitute the values from the data, then solve to find the slope.

00:29 Great! Now, we know the slope of the graph.

00:34 Let's use this slope in the linear equation.

00:37 Substitute the values again, solve to find B. B is the Y-intercept.

00:49 Now, we know both the slope and the Y-intercept.

00:55 We'll write the linear equation using these values.

00:59 And there you have it! That's the solution to our problem.

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 match the graph to the correct equation, we will analyze the slope and y-intercept:

Step 1: Identify y-intercept.
From the graph, observe that the line crosses the y-axis at $y = 4$ . Therefore, the y-intercept $b = 4$ .
Step 2: Calculate slope.
Identify two points on the graph line, such as $(0, 4)$ and $(5, 0)$ . Calculate slope using $m = \frac{\Delta y}{\Delta x}$ :
$m = \frac{0 - 4}{5 - 0} = \frac{-4}{5}$ .
**Step 3: Match to equations**.
Now we have $m = -\frac{4}{5}$ and $b = 4$ , so the equation should be $y = -\frac{4}{5}x + 4$ .

After comparing with the choices, we see that choice $(2)$ $y = -\frac{4}{5}x + 4$ correctly matches the information derived from the graph.

Therefore, the equation that corresponds to the graph is $y = -\frac{4}{5}x + 4$ .

3

Final Answer

$y=-\frac{4}{5}x+4$

Key Points to Remember

Essential concepts to master this topic

Y-Intercept: Find where the line crosses the y-axis
Slope Formula: Use $m = \frac{\Delta y}{\Delta x} = \frac{0-4}{5-0} = -\frac{4}{5}$
Verification: Check that your equation passes through both identified points ✓

Common Mistakes

Avoid these frequent errors

Mixing up rise and run when calculating slope
Don't calculate slope as run over rise = wrong sign and value! This gives you the reciprocal with opposite sign. Always use rise over run: change in y divided by change in x.

Practice Quiz

Test your knowledge with interactive questions

Determine whether the given graph is a function?

FAQ

Everything you need to know about this question

How do I know which direction is positive for slope?

+

Moving left to right: if the line goes up, slope is positive; if it goes down, slope is negative. In this graph, the line falls from left to right, so the slope is negative.

What if I can't see exact points on the grid?

+

Look for points where the line passes through grid intersections. In this case, (0,4) and (5,0) are clear intersection points that make calculations easier.

Why is the slope -4/5 and not -5/4?

+

Slope is always $\frac{\text{rise}}{\text{run}}$ . From (0,4) to (5,0): we go down 4 units (rise = -4) and right 5 units (run = +5), giving us $\frac{-4}{5}$ .

How do I find the y-intercept from a graph?

+

The y-intercept is where the line crosses the y-axis (when x = 0). Look at the graph and see what y-value the line passes through on the vertical axis.

Can I use any two points to find the slope?

+

Yes! Any two points on the line will give you the same slope. Choose points that are easy to read from the graph, preferably at grid intersections.

What does the negative slope tell me about the line?

+

A negative slope means the line is decreasing - as x-values increase, y-values decrease. The line slants downward from left to right.

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Identify the Linear Equation with a Slope of -1 from the Graph

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