Drag a number to each box to represent the equation of the line.

Understand the Problem

The question is asking to determine the equation of a line shown on a coordinate plane. To solve this, we need to identify the slope and the y-intercept from the graph provided. The equation will take the form y = mx + b, where m is the slope and b is the y-intercept.

Answer

The equation is $y = -2x + 10$.

Steps to Solve

Identify the y-intercept

Look at the graph to find where the line crosses the y-axis. This point will give you the value of $b$ in the equation $y = mx + b$. From the graph, it appears the line crosses the y-axis at $10$, so $b = 10$.

Determine the slope

Next, we need to calculate the slope $m$. The slope is determined by the formula:

$$ m = \frac{\text{rise}}{\text{run}} $$

Select two points on the line. For example, we can choose the points $(1, 10)$ and $(2, 8)$. The rise from $(1, 10)$ to $(2, 8)$ is $8 - 10 = -2$ and the run is $2 - 1 = 1$.

Calculating the slope:

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

Write the equation

Now, substitute the values of $m$ and $b$ into the equation $y = mx + b$. This gives us:

$$ y = -2x + 10 $$

The equation of the line is $y = -2x + 10$.

More Information

This equation indicates a line with a negative slope, meaning it decreases as $x$ increases. The y-intercept of 10 tells us where the line intersects the y-axis (the value of $y$ when $x = 0$).

Tips

Mistaking the direction of the slope: Remember that if the line goes up from left to right, the slope is positive; if it goes down, it's negative.
Incorrectly identifying the y-intercept; double-check the point where the line crosses the y-axis.

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