find the equation of the line with slope -2 and y-intercept 3/4 and how to graph

To find the equation of a line given its slope and y-intercept, you can use the **slope-intercept form** of the equation of a line:

\[
y = mx + b
\]

Where:
- \( m \) is the slope,
- \( b \) is the y-intercept.

Given:
- Slope \( m = -2 \),
- Y-intercept \( b = \frac{3}{4} \).

Substituting these values into the slope-intercept form:

\[
y = -2x + \frac{3}{4}
\]

### How to Graph the Line:
1. **Plot the y-intercept**: Start by plotting the point \( \left(0, \frac{3}{4}\right) \) on the y-axis.
   
2. **Use the slope**: The slope of -2 means that for every 1 unit you move to the right (along the x-axis), you move 2 units down (since the slope is negative).
   
3. **Plot a second point**: Starting from the y-intercept \( (0, \frac{3}{4}) \), move 1 unit to the right and 2 units down to plot another point. This point will be \( (1, -\frac{5}{4}) \).

4. **Draw the line**: Use a straight edge to connect the two points and extend the line in both directions.

Would you like a more detailed graphing procedure or any other clarification?

### 5 Related Questions:
1. How do you determine the slope of a line from two points?
2. What is the equation of a line parallel to \( y = -2x + \frac{3}{4} \)?
3. How do you convert the equation of a line from slope-intercept form to standard form?
4. What is the difference between slope-intercept form and point-slope form?
5. How do you find the x-intercept of the line \( y = -2x + \frac{3}{4} \)?

**Tip:** When graphing lines, always remember that the slope indicates the steepness and direction of the line.

Find the equation of the line with slope -2 and y-intercept 3/4 and how to graph it.

Learn how to find the equation of a line with a slope of -2 and y-intercept 3/4 using the slope-intercept form. This step-by-step solution explains the concept and provides tips on how to graph the line. Suitable for students in Grades 7-9.

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