To find the equation of a line in slope-intercept form given a slope and a y-intercept, you can use the formula for slope-intercept form, which is:
[tex]\[ y = mx + b \][/tex]
where:
- [tex]\( m \)[/tex] is the slope
- [tex]\( b \)[/tex] is the y-intercept
In this case, you are given a slope ([tex]\( m \)[/tex]) of [tex]\(-\frac{3}{2}\)[/tex] and a y-intercept ([tex]\( b \)[/tex]) of [tex]\(-3\)[/tex].
Substitute the given values into the slope-intercept form equation:
[tex]\[ y = \left( -\frac{3}{2} \right)x + (-3) \][/tex]
This can be written more clearly as:
[tex]\[ y = -\frac{3}{2}x - 3 \][/tex]
Therefore, the equation of the line in slope-intercept form is:
[tex]\[ y = -1.5x + -3 \][/tex]
