Question
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Answer
The equation of the line is \( y = x + 8 \).
Solution
To find the equation of a line given the slope and the y-intercept, we can use the slope-intercept form of a linear equation, which is given by:
\[
y = mx + b
\]
where:
- \( m \) is the slope,
- \( b \) is the y-intercept.
From the problem, we have:
- Slope \( m = 1 \)
- Y-intercept \( b = 8 \)
Now, we can substitute these values into the equation:
\[
y = 1x + 8
\]
This simplifies to:
\[
y = x + 8
\]
Thus, the equation of the line is:
\[
\boxed{y = x + 8}
\]
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Simplify this solution Mind Expander
Did you know that the equation of a line can be expressed in the form \( y = mx + b \), where \( m \) represents the slope and \( b \) the y-intercept? For your line with a slope of 1 and a y-intercept of 8, the equation would be \( y = 1x + 8 \) or simply \( y = x + 8 \). This means that for every unit increase in \( x \), \( y \) increases by the same amount! When graphing this line, start at the point where it crosses the y-axis at (0,8). From there, you can use the slope to navigate: rise 1 unit up and run 1 unit to the right to find the next points on the line! It’s like plotting your own treasure map across the coordinate plane!
