Certainly! Let's follow the steps to convert the given point-slope form equation to the slope-intercept form.
Start with the given equation in point-slope form:
[tex]\[ y - 4 = -3(x - 2) \][/tex]
1. Distribute the [tex]\(-3\)[/tex] on the right-hand side:
[tex]\[ y - 4 = -3x + 6 \][/tex]
2. To isolate [tex]\( y \)[/tex], add 4 to both sides:
[tex]\[ y - 4 + 4 = -3x + 6 + 4 \][/tex]
3. Simplify the equation by combining like terms:
[tex]\[ y = -3x + 10 \][/tex]
So, the equation in slope-intercept form [tex]\( y = mx + b \)[/tex] is:
[tex]\[ y = -3x + 10 \][/tex]
From this equation, we can identify the slope [tex]\( m \)[/tex] and the y-intercept [tex]\( b \)[/tex]:
[tex]\[ m = -3 \][/tex]
[tex]\[ b = 10 \][/tex]
So the values are:
[tex]\[ \boxed{-3, 10} \][/tex]
