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?

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.

1. **First line:**  
   Given: The gradient (slope) is \(-1\) and the y-intercept is \(5\).  
   The equation of the first line can be written as:
   \[
   y = -x + 5
   \]

2. **Second line:**  
   The equation of the second line is given as:
   \[
   y = 0.5x + 2
   \]

### Step 2: Set the equations equal to find the intersection.
To find the point of intersection, set the two equations equal to each other:
\[
-x + 5 = 0.5x + 2
\]

### Step 3: Solve for \(x\).
To solve for \(x\), first, get all the terms involving \(x\) on one side:
\[
5 - 2 = 0.5x + x
\]
\[
3 = 1.5x
\]
\[
x = \frac{3}{1.5} = 2
\]

### Step 4: Find the corresponding \(y\) value.
Now that we have \(x = 2\), substitute it back into either equation to find the corresponding \(y\) value. Let's use the first equation:
\[
y = -2 + 5 = 3
\]

### Conclusion: Intersection point
The two lines intersect at the point \((2, 3)\).

Would you like more details, or do you have any questions?

Here are 5 related questions:
1. How do you determine the gradient of a line from two given points?
2. What is the geometric interpretation of the y-intercept of a line?
3. How can you determine if two lines are parallel?
4. How do you find the equation of a line given its slope and a point on the line?
5. 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.

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?

Learn how to find the intersection point of two lines given their equations, one with a slope of -1 and a y-intercept of 5, and the other with the equation y = 0.5x + 2. This problem is ideal for students in Grades 8-10 and covers key algebraic concepts such as the slope-intercept form and solving systems of linear equations.

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