Math Problem Statement

Find the equation of the line parallel to y = -3x + 2 passing through point (-8, -1).

Solution

The image contains a problem asking to find the equation of a line parallel to the line y=3x+2y = -3x + 2 and passing through the point (8,1)(-8, -1).

To solve this:

  1. Identify the slope of the given line y=3x+2y = -3x + 2, which is the coefficient of xx. This is m=3m = -3.

  2. Use the point-slope form of the equation of a line, which is:

yy1=m(xx1)y - y_1 = m(x - x_1)

Where mm is the slope and (x1,y1)(x_1, y_1) is the point through which the line passes. Here, the point is (8,1)(-8, -1) and the slope is m=3m = -3.

  1. Substitute the values into the point-slope form:

y(1)=3(x(8))y - (-1) = -3(x - (-8))

Simplifying:

y+1=3(x+8)y + 1 = -3(x + 8)

  1. Distribute the slope:

y+1=3x24y + 1 = -3x - 24

  1. Solve for yy by subtracting 1 from both sides:

y=3x25y = -3x - 25

Thus, the equation of the line parallel to y=3x+2y = -3x + 2 passing through (8,1)(-8, -1) is:

y=3x25y = -3x - 25

Would you like further clarification or have any additional questions on this problem? Here are some related questions you can explore:

  1. How do you find the slope of a line from its equation?
  2. What is the point-slope form of the equation of a line?
  3. How do you convert from point-slope form to slope-intercept form?
  4. How do parallel lines relate to their slopes?
  5. How do you find the equation of a line passing through a point with a given slope?

Tip: When writing the equation of a line, always check that you use the correct form depending on the information given (e.g., point-slope, slope-intercept).

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Linear Equations
Point-Slope Form
Slope-Intercept Form

Formulas

y - y1 = m(x - x1)
Slope-intercept form: y = mx + b

Theorems

Parallel Lines Theorem

Suitable Grade Level

Grades 8-10