Math Problem Statement

Write the equation of the line that passes through the points left parenthesis, minus, 7, comma, 0, right parenthesis(−7,0) and left parenthesis, minus, 3, comma, minus, 4, right parenthesis(−3,−4). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

Solution

To find the equation of the line passing through the points (7,0)(-7, 0) and (3,4)(-3, -4), follow these steps:

  1. Calculate the slope (mm) of the line using the formula: m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1} where (x1,y1)=(7,0)(x_1, y_1) = (-7, 0) and (x2,y2)=(3,4)(x_2, y_2) = (-3, -4).

    m=403(7)=43+7=44=1m = \frac{-4 - 0}{-3 - (-7)} = \frac{-4}{-3 + 7} = \frac{-4}{4} = -1

  2. Use the point-slope form of the equation of a line, which is: yy1=m(xx1)y - y_1 = m(x - x_1)

    Substitute the slope m=1m = -1 and one of the points, say (7,0)(-7, 0):

    y0=1(x(7))y - 0 = -1(x - (-7))

  3. Simplify the equation: y=1(x+7)y = -1(x + 7)

    y=x7y = -x - 7

So, the equation of the line in point-slope form is: y=x7y = -x - 7

Would you like further details or have any questions?

Here are some related questions you might find helpful:

  1. How do you convert this equation to standard form?
  2. What is the y-intercept of this line?
  3. How would you graph this line?
  4. What is the equation of a line parallel to this one that passes through a different point?
  5. How would the equation change if the slope were positive instead of negative?

Tip: Always remember to simplify the slope as much as possible before using it in the point-slope form.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Point-Slope Form

Formulas

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

Theorems

Point-Slope Equation of a Line

Suitable Grade Level

Grades 8-10