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I see that you have uploaded an image of a worksheet for graphing linear equations. The instructions mention plotting lines with various given conditions. Let's break down the tasks step by step:

### Tasks:
1. **Line through (-5, -2) and intersecting the x-axis at -4**: 
   - You have two points: (-5, -2) and (-4, 0) (x-intercept).
   - Use the slope formula \(\frac{y_2 - y_1}{x_2 - x_1}\) to find the slope.
   - Then use the point-slope form \(y - y_1 = m(x - x_1)\) to find the equation of the line.

2. **Line with y-intercept 3 and x-intercept -8**:
   - The slope can be found by using the points (0, 3) and (-8, 0).
   - Again, use the slope formula and then find the equation using point-slope form or slope-intercept form \(y = mx + b\).

3. **Given equation \(y = -\frac{3}{8}x + 3\)**:
   - Simply graph this by identifying the slope and y-intercept.

4. **Line with y-intercept -3, parallel to line 2**:
   - A line parallel to line 2 will have the same slope as line 2.
   - Use this slope and the given y-intercept to write the equation in slope-intercept form.

5. **Line with y-intercept 8 and slope 1**:
   - The equation is \(y = x + 8\).

6. **Line with y-intercept -8 and slope -2**:
   - The equation is \(y = -2x - 8\).

7. **Line with x-intercept 8 and y-intercept 8**:
   - Use the points (8, 0) and (0, 8) to find the slope.
   - Write the equation using the slope and one of the points.

8. **Line parallel to line 3 with y-intercept -3**:
   - The slope will be \(-\frac{3}{8}\), same as line 3.
   - The equation will be \(y = -\frac{3}{8}x - 3\).

9. **Line through points (-6, 2) and (-1, 7)**:
   - Use the slope formula and then the point-slope form to find the equation.

10. **Line through the x-intercept of line 9 with slope -1**:
   - First, find the x-intercept of line 9 by solving the equation when \(y = 0\).
   - Use this point and the slope -1 to find the equation.

11. **Line with y-intercept 8 and slope -2**:
   - The equation is \(y = -2x + 8\).

12. **Line passing through (5, 2) and the y-intercept of line 6**:
   - First, find the y-intercept of line 6 (which is -8).
   - Use these two points, (5, 2) and (0, -8), to find the slope and equation.

Would you like a detailed solution for any of the lines, or do you need assistance with graphing? 

### 5 Related Questions:
1. How do you calculate the slope between two points?
2. What is the point-slope form of a linear equation?
3. How do you determine if two lines are parallel or perpendicular?
4. What does it mean if a line has an undefined slope?
5. How do you graph a line given its slope and intercept?

### Tip:
When graphing lines, always start by plotting the intercepts (if known) and then use the slope to find additional points. This helps to ensure accuracy in drawing the line.

Graph each line on the grid to make a pattern. Use a ruler to see the neat effect! Number each line.

Learn how to graph linear equations by finding the slope, y-intercept, and x-intercept. This problem set explores key algebraic concepts such as graphing lines, determining the equations of lines through given points, and understanding parallel lines. Suitable for students in Grades 8-10.

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