Write an equation in slope-intercept form for the line with slope 5 and [tex]y[/tex]-intercept -1.

[tex]y = 5x - 1[/tex]



Answer :

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]