Certainly! Let's write the equation of a line in the slope-intercept form, given the specific values for the slope and the [tex]$y$[/tex]-intercept.
1. Understanding the slope-intercept form:
The slope-intercept form of a line is given by the equation:
[tex]\[
y = mx + b
\][/tex]
where [tex]\( m \)[/tex] represents the slope and [tex]\( b \)[/tex] represents the [tex]$y$[/tex]-intercept.
2. Given values:
- The slope ([tex]\( m \)[/tex]) is 5.
- The [tex]$y$[/tex]-intercept ([tex]\( b \)[/tex]) is -1.
3. Substituting the values into the slope-intercept form:
We replace [tex]\( m \)[/tex] with 5 and [tex]\( b \)[/tex] with -1 in the equation:
[tex]\[
y = 5x + (-1)
\][/tex]
4. Simplifying the equation if necessary:
The equation simplifies to:
[tex]\[
y = 5x - 1
\][/tex]
Therefore, the equation in slope-intercept form for the line with slope 5 and [tex]$y$[/tex]-intercept -1 is:
[tex]\[
y = 5x - 1
\][/tex]
