To write the equation of a line in slope-intercept form, we use the formula [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope of the line and [tex]\( b \)[/tex] is the y-intercept.
Given:
- A point on the line [tex]\((-6, -1)\)[/tex]
- The slope [tex]\( m = -3 \)[/tex]
First, we substitute the given point [tex]\((-6, -1)\)[/tex] and the slope [tex]\( m = -3 \)[/tex] into the general slope-intercept form to find [tex]\( b \)[/tex] (the y-intercept).
Using the coordinates of the point:
[tex]\[ y = -1 \][/tex]
[tex]\[ x = -6 \][/tex]
Using the slope [tex]\( m = -3 \)[/tex], substitute these values into the slope-intercept formula:
[tex]\[ y = mx + b \][/tex]
[tex]\[ -1 = -3(-6) + b \][/tex]
Simplify the equation:
[tex]\[ -1 = 18 + b \][/tex]
Solve for [tex]\( b \)[/tex]:
[tex]\[ -1 - 18 = b \][/tex]
[tex]\[ b = -19 \][/tex]
We now have the slope [tex]\( m = -3 \)[/tex] and the y-intercept [tex]\( b = -19 \)[/tex].
Therefore, the equation of the line in slope-intercept form is:
[tex]\[ y = -3x - 19 \][/tex]
