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.