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 and , follow these steps:
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Calculate the slope () of the line using the formula: where and .
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Use the point-slope form of the equation of a line, which is:
Substitute the slope and one of the points, say :
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Simplify the equation:
So, the equation of the line in point-slope form is:
Would you like further details or have any questions?
Here are some related questions you might find helpful:
- How do you convert this equation to standard form?
- What is the y-intercept of this line?
- How would you graph this line?
- What is the equation of a line parallel to this one that passes through a different point?
- 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
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