A line has a slope of 1 and passes through the point (6,10).Write its equation in slope-intercept form.

To write the equation of a line in slope-intercept form, which is \( y = mx + b \), we need two things:
1. The slope \( m \)
2. The y-intercept \( b \)

Given:
- Slope \( m = 1 \)
- Point \( (6, 10) \) on the line

### Step 1: Substitute the slope and point into the slope-intercept form
Using the point \((6, 10)\):
\[
y = mx + b
\]
Substitute \( y = 10 \), \( x = 6 \), and \( m = 1 \):
\[
10 = 1 \cdot 6 + b
\]

### Step 2: Solve for \( b \)
\[
10 = 6 + b
\]
\[
b = 4
\]

### Step 3: Write the final equation
Now that we have the slope \( m = 1 \) and the y-intercept \( b = 4 \), the equation of the line is:
\[
y = x + 4
\]

Let me know if you would like a further breakdown or have any questions!

### Related Questions
1. What is the equation of a line with slope \( 2 \) passing through the point \( (3, 7) \)?
2. How do you find the equation of a line if given two points on the line?
3. What is the slope-intercept form of a line parallel to \( y = 2x + 5 \) passing through \( (1, 3) \)?
4. How would the equation change if the slope were \(-1\) instead of \(1\)?
5. What is the equation of a line with an undefined slope passing through \( (6, 10) \)?

### Tip
Remember, in slope-intercept form, the slope \( m \) determines the angle of the line, while the y-intercept \( b \) shifts it up or down on the graph.

A line has a slope of 1 and passes through the point (6,10). Write its equation in slope-intercept form.

Discover how to write the equation of a line with a slope of 1 that passes through the point (6, 10) in slope-intercept form. This problem includes essential algebraic concepts, such as slope-intercept form and solving for the y-intercept. Ideal for students in Grades 8-10.

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