To write the point-slope equation for a line with the given slope and a point on the line, we will use the point-slope form of the equation:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Here, [tex]\( m \)[/tex] is the slope of the line, and [tex]\((x_1, y_1)\)[/tex] is the given point on the line.
Given:
[tex]\[ \text{Slope} = 8 \][/tex]
[tex]\[ \text{Point on line} = (5, 6) \][/tex]
Let's substitute these values into the point-slope form equation:
1. Identify the slope [tex]\( m \)[/tex]:
[tex]\[ m = 8 \][/tex]
2. Identify the coordinates of the given point [tex]\((x_1, y_1)\)[/tex]:
[tex]\[ x_1 = 5 \][/tex]
[tex]\[ y_1 = 6 \][/tex]
3. Substitute [tex]\( m \)[/tex], [tex]\( x_1 \)[/tex], and [tex]\( y_1 \)[/tex] into the point-slope form equation:
[tex]\[ y - 6 = 8(x - 5) \][/tex]
Hence, the point-slope equation of the line is:
[tex]\[ y - 6 = 8(x - 5) \][/tex]
This equation represents the line with a slope of 8 passing through the point (5, 6).
