Math Problem Statement

What is an equation of the line that passes through the points (0, -6) and (1, 0)?

Solution

The question asks for the equation of the line that passes through the points (0,6)(0, -6) and (1,0)(1, 0). Let's solve it step by step.

Step 1: Calculate the slope (mm) of the line

The slope formula is: m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1} Substitute (x1,y1)=(0,6)(x_1, y_1) = (0, -6) and (x2,y2)=(1,0)(x_2, y_2) = (1, 0): m=0(6)10=61=6m = \frac{0 - (-6)}{1 - 0} = \frac{6}{1} = 6

Step 2: Use the point-slope form of a line

The point-slope form of a line is: yy1=m(xx1)y - y_1 = m(x - x_1) Substitute m=6m = 6 and one of the points, say (0,6)(0, -6), into the formula: y(6)=6(x0)y - (-6) = 6(x - 0) Simplify: y+6=6xy + 6 = 6x

Step 3: Write the equation in slope-intercept form

Simplify further to get: y=6x6y = 6x - 6

Final Answer:

The equation of the line is: y=6x6y = 6x - 6


Would you like a detailed explanation for any of the steps?

Here are 5 related questions to expand your understanding:

  1. How do you find the slope of a vertical line?
  2. What is the equation of a line that passes through two points with the same yy-coordinate?
  3. How can you convert an equation in point-slope form to standard form?
  4. What is the geometric interpretation of the slope of a line?
  5. How would the equation change if one of the points were shifted?

Tip:

When solving for the equation of a line, double-check your slope calculation—it determines the steepness of the line!

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Slope-Intercept Form
Point-Slope Form

Formulas

Slope formula: m = (y2 - y1) / (x2 - x1)
Point-slope form: y - y1 = m(x - x1)
Slope-intercept form: y = mx + b

Theorems

Equation of a Line Theorem

Suitable Grade Level

Grades 8-10