Math Problem Statement
Write the equation of the line that passes through the points left parenthesis, 9, comma, minus, 1, right parenthesis(9,−1) and left parenthesis, minus, 7, comma, 4, right parenthesis(−7,4). 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 , we follow these steps:
1. Find the slope of the line (denoted by ):
The formula for the slope between two points and is:
Substituting the given points and :
2. Use the point-slope form of the equation of a line:
The point-slope form is given by:
Using the point and the slope :
Simplifying the equation:
This is the equation of the line in point-slope form.
Would you like more details on solving it further, or have any questions?
Here are 5 related questions:
- How do you convert from point-slope form to slope-intercept form?
- What happens when the line is vertical or horizontal?
- How can you check if a point lies on a line?
- How do you find the distance between two points?
- How do you find the equation of a line parallel to a given line?
Tip: The slope of a vertical line is undefined, while a horizontal line has a slope of zero.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Point-Slope Form
Slope of a Line
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Point-slope form: y - y1 = m(x - x1)
Theorems
Slope-Intercept Theorem
Suitable Grade Level
Grades 8-10
Related Recommendation
Equation of a Line Passing Through Points (-3,-7) and (9,1)
Equation of a Line through Points (7, 8) and (9, -9) in Point-Slope Form
Equation of a Line Through Points (-4, 7) and (2, -1)
Equation of a Line Through Points (9, -4) and (2, -2) in Point-Slope Form
Equation of a Line Through Points (2,-1) and (4,2)