Math Problem Statement
A line has a slope of 7. For each pair of points in problems 9 to 12 that are on the line, use the slope formula to find the missing coordinate. (x, 8) and (4, 1) : (3,-6) and (7,y)
Solution
To find the missing coordinates using the slope formula, we use the formula for the slope of a line:
Given that the slope , we'll use this formula to solve for the missing coordinates.
Problem 1: and
The slope is 7, and we know the points and . Using the slope formula:
This simplifies to:
Now, solve for :
So, the missing coordinate for the first pair is .
Problem 2: and
Again, the slope is 7, and we know the points and . Using the slope formula:
This simplifies to:
Now, solve for :
So, the missing coordinate for the second pair is .
Summary:
- For and ,
- For and ,
Would you like further details on the solution or any clarifications? Here are 5 related questions for practice:
- Find the slope between the points and .
- Given the points and , and a slope of 2, find .
- Find the equation of the line passing through and .
- If a line has a slope of 3 and passes through , find its equation in slope-intercept form.
- Given two points and , what happens to the slope if ?
Tip: Remember, when two points have the same x-coordinates, the slope is undefined because you cannot divide by zero!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Coordinate Geometry
Linear Equations
Slope
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Theorems
Slope of a Line
Suitable Grade Level
Grades 8-10
Related Recommendation
Find the Missing Coordinate for a Line with a Given Slope
Finding Missing Coordinate with Given Slope and Points
Find the Missing Coordinate Using Slope and Point-Slope Formula
How to Find the Slope of a Line Through Two Points (8, 7) and (4, 4)
Calculating Slopes of Lines Given Points: Step-by-Step Solution