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.