We are given the equation:

$y = -\frac{7}{10}$

Step 1: Identify the Slope

This equation represents a horizontal line because there is no $x$-term.

• The general form of a linear equation is $y = mx + b$, where:

  • $m$ is the slope.
  • $b$ is the y-intercept.

• Comparing with $y = -\frac{7}{10}$, we see that:

  • The slope $m = 0$ (since there's no $x$-term).
  • The equation remains constant for all values of $x$, meaning it is a horizontal line.

Answer:

• Slope = 0 → Choice A: The slope is 0.

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Step 2: Identify the y-Intercept

The given equation can be rewritten as:

$y = 0x - \frac{7}{10}$

• The y-intercept ($b$) is the constant term, which is $-\frac{7}{10}$.
• This means the line crosses the y-axis at $(0, -\frac{7}{10})$.

Answer:

• y-Intercept = $-\frac{7}{10}$ → Choice A: The y-intercept is $-\frac{7}{10}$.

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Step 3: Graph the Equation

To graph $y = -\frac{7}{10}$:

1. Plot the y-intercept at $(0, -\frac{7}{10})$.
2. Since the slope is 0, the line remains horizontal across the entire graph.
3. Draw a horizontal line passing through $y = -\frac{7}{10}$.

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Final Answers:

• Slope: $0$
• y-Intercept: $-\frac{7}{10}$
• Graph: A horizontal line at $y = -\frac{7}{10}$.

Would you like me to generate a graph for better visualization?

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Related Questions

1. How do you determine if a line is horizontal or vertical?
2. What happens if the slope is undefined?
3. How can we express horizontal and vertical lines in standard form?
4. What are real-life examples of horizontal lines?
5. How do you graph an equation when the slope is a fraction?

Math Tip:

A horizontal line has the form $y = b$ and always has a slope of 0 because the rise is zero regardless of the run.