Math Problem Statement

Write an equation, in point-slope form, of the line that passes through the given points: ( 1, - 8 ) ( 2, - 5 )

Solution

To write the equation of a line in point-slope form, we need to follow these steps:

  1. Find the slope of the line that passes through the points (1,8)(1, -8) and (2,5)(2, -5).
    The slope formula is:

    m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}

    Substituting the given points into the formula:

    m=5(8)21=5+81=31=3m = \frac{-5 - (-8)}{2 - 1} = \frac{-5 + 8}{1} = \frac{3}{1} = 3

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

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

    We can use either of the given points. Let's use (1,8)(1, -8):

    y(8)=3(x1)y - (-8) = 3(x - 1)

  3. Simplify the equation:

    y+8=3(x1)y + 8 = 3(x - 1)

This is the equation of the line in point-slope form.

Would you like a more detailed explanation, or do you have any other questions?

Here are 5 related questions for further practice:

  1. Write the equation in slope-intercept form for the same line.
  2. Find the equation of a line passing through the points (3,7)(3, 7) and (5,11)(5, 11).
  3. Determine the slope of a line that is perpendicular to the line passing through (1,8)(1, -8) and (2,5)(2, -5).
  4. Write the equation of the line with a slope of 4 that passes through the point (0,2)(0, -2).
  5. Find the point of intersection between the line passing through (1,8)(1, -8) and (2,5)(2, -5) and the line y=2x+3y = 2x + 3.

Tip: The point-slope form is especially useful when you know a point on the line and its slope, allowing for quick equation writing without rearranging to slope-intercept form immediately.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Linear Equations
Slope
Point-Slope Form

Formulas

Slope formula
Point-Slope Form equation

Theorems

-

Suitable Grade Level

Grades 7-9