Sure! To write the equation of a line in point-slope form, we use the formula:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
where [tex]\((x_1, y_1)\)[/tex] is a point on the line and [tex]\( m \)[/tex] is the slope of the line.
1. Identify the given point and the slope:
- The given point is [tex]\((-6, 8)\)[/tex], so [tex]\( x_1 = -6 \)[/tex] and [tex]\( y_1 = 8 \)[/tex].
- The given slope is [tex]\( m = \frac{3}{2} \)[/tex].
2. Substitute the values into the point-slope form equation:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Substitute [tex]\( x_1 = -6 \)[/tex], [tex]\( y_1 = 8 \)[/tex], and [tex]\( m = \frac{3}{2} \)[/tex]:
[tex]\[ y - 8 = \frac{3}{2}(x - (-6)) \][/tex]
3. Simplify the equation (if necessary):
- Notice that [tex]\( x - (-6) \)[/tex] simplifies to [tex]\( x + 6 \)[/tex].
So, the equation in point-slope form is:
[tex]\[ y - 8 = \frac{3}{2}(x + 6) \][/tex]
Alternatively, expressing with decimal multiplication:
[tex]\[ y - 8 = 1.5(x + 6) \][/tex]
Thus, the point-slope form of the equation for the line passing through the point [tex]\((-6, 8)\)[/tex] with a slope of [tex]\(\frac{3}{2}\)[/tex] is:
[tex]\[ y - 8 = 1.5(x + 6) \][/tex]
