Math Problem Statement

Use point-slope form to write the equation of a line that passes through the point left parenthesis, 6, comma, 7, right parenthesis(6,7) with slope minus, 3−3.

Solution

The point-slope form of a line is given by the formula:

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

where:

  • (x1,y1)(x_1, y_1) is a point on the line,
  • mm is the slope of the line.

Given:

  • Point: (6,7)(6, 7),
  • Slope: 3-3,

we substitute these values into the formula:

y7=3(x6)y - 7 = -3(x - 6)

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

If you'd like, we can expand it to the slope-intercept form (y=mx+by = mx + b).

Do you want further details or have any questions?

Here are 5 related questions:

  1. How can we convert this equation into slope-intercept form?
  2. What is the slope-intercept form of a line, and how does it relate to point-slope form?
  3. How do we graph the line using the point (6,7)(6, 7) and the slope 3-3?
  4. How do we find the x-intercept and y-intercept from this equation?
  5. Can we use a different point on the line to write the equation again in point-slope form?

Tip: The point-slope form is especially useful when you know the slope and one point on the line, as it avoids having to find the y-intercept directly.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Point-Slope Form

Formulas

Point-slope form: y - y1 = m(x - x1)

Theorems

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Suitable Grade Level

Grades 8-10