Step 1: Determine if the Equation is Linear

The given equation is:

$y = \frac{1}{2}x - 5$

This equation is in the slope-intercept form of a linear equation:

$y = mx + b$

where:

• $m = \frac{1}{2}$ (the slope)
• $b = -5$ (the y-intercept)

Since the equation follows the standard form of a linear equation, it is a linear equation.

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Step 2: Find Ordered-Pair Solutions

To graph the equation, we choose values for $x$ and calculate $y$.

Choose $x = 0$:

$y = \frac{1}{2}(0) - 5 = -5$ Ordered pair: $(0, -5)$

Choose $x = 2$:

$y = \frac{1}{2}(2) - 5 = 1 - 5 = -4$ Ordered pair: $(2, -4)$

Choose $x = 4$:

$y = \frac{1}{2}(4) - 5 = 2 - 5 = -3$ Ordered pair: $(4, -3)$

Choose $x = -2$:

$y = \frac{1}{2}(-2) - 5 = -1 - 5 = -6$ Ordered pair: $(-2, -6)$

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Step 3: Graph the Equation

1. Plot the points: $(0, -5)$, $(2, -4)$, $(4, -3)$, and $(-2, -6)$.
2. Draw a straight line through these points since it is a linear equation.
3. Extend the line in both directions.

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Would you like me to generate a graph for you? Also, do you need more details?

Related Questions:

1. How do you determine if an equation is linear from its standard form?
2. What is the significance of the slope and y-intercept in a linear equation?
3. How do you find the x-intercept of a linear equation?
4. What happens to the graph if the slope changes?
5. How can you convert a linear equation from slope-intercept form to standard form?

Tip:

To quickly check if an equation is linear, ensure that both $x$ and $y$ have a power of 1 and are not multiplied together.