Math Problem Statement
A straight line has a gradient of -1 and intercepts the y-axis at 5. A second line has the equation of y=0.5+2. where do these two lines intersect?
Solution
To find the intersection of the two lines, we need to solve the system of equations formed by their respective equations.
Step 1: Identify the equations of the two lines.
-
First line:
Given: The gradient (slope) is and the y-intercept is .
The equation of the first line can be written as: -
Second line:
The equation of the second line is given as:
Step 2: Set the equations equal to find the intersection.
To find the point of intersection, set the two equations equal to each other:
Step 3: Solve for .
To solve for , first, get all the terms involving on one side:
Step 4: Find the corresponding value.
Now that we have , substitute it back into either equation to find the corresponding value. Let's use the first equation:
Conclusion: Intersection point
The two lines intersect at the point .
Would you like more details, or do you have any questions?
Here are 5 related questions:
- How do you determine the gradient of a line from two given points?
- What is the geometric interpretation of the y-intercept of a line?
- How can you determine if two lines are parallel?
- How do you find the equation of a line given its slope and a point on the line?
- What does it mean for two lines to be perpendicular?
Tip: When solving systems of linear equations, setting the equations equal to each other is a key step in finding the intersection.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Intersection of Lines
Formulas
Equation of a line: y = mx + c
Theorems
Slope-Intercept Form
Suitable Grade Level
Grades 8-10
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