Math Problem Statement

Write a slope-intercept equation for a line passing through the points (-7, 0) and (4, -2).

Solution

The task asks to write a slope-intercept equation for a line that passes through the points (-7, 0) and (4, -2).

Steps to solve:

  1. Find the slope (mm) of the line using the slope formula: m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1} Here, (x1,y1)=(7,0)(x_1, y_1) = (-7, 0) and (x2,y2)=(4,2)(x_2, y_2) = (4, -2).

    Substituting the values: m=204(7)=24+7=211m = \frac{-2 - 0}{4 - (-7)} = \frac{-2}{4 + 7} = \frac{-2}{11} So, the slope is m=211m = -\frac{2}{11}.

  2. Use the point-slope form of the equation to find the equation of the line: yy1=m(xx1)y - y_1 = m(x - x_1) Using the point (7,0)(-7, 0) and the slope m=211m = -\frac{2}{11}: y0=211(x(7))=211(x+7)y - 0 = -\frac{2}{11}(x - (-7)) = -\frac{2}{11}(x + 7)

  3. Simplify to slope-intercept form (y=mx+by = mx + b): y=211(x+7)y = -\frac{2}{11}(x + 7) Distribute the 211-\frac{2}{11}: y=211x1411y = -\frac{2}{11}x - \frac{14}{11}

Thus, the slope-intercept form of the equation is: y=211x1411y = -\frac{2}{11}x - \frac{14}{11}

Would you like a detailed explanation of any of the steps? Let me know!

Here are 5 questions that expand on the topic:

  1. How do you find the y-intercept from two points?
  2. Can you derive the slope-intercept form directly from the two points without using point-slope form?
  3. What does the slope of a line tell you about its direction and steepness?
  4. How would the equation change if the line passed through different points?
  5. Can a line have an undefined slope? If so, what does that line look like?

Tip: When solving for the slope, be careful with signs and subtraction, as they can easily affect your final result.

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Math Problem Analysis

Mathematical Concepts

Algebra
Coordinate Geometry
Linear Equations

Formulas

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

Theorems

Slope-intercept form theorem

Suitable Grade Level

Grades 8-10