Answer :
To find the point-slope form of a line, we use the formula:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
where [tex]\((x_1, y_1)\)[/tex] is a given point on the line and [tex]\(m\)[/tex] is the slope.
Given the slope [tex]\(m = 6\)[/tex] and the point [tex]\((1, 2)\)[/tex], we can substitute these values into the formula:
1. Start with the point-slope formula:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
2. Substitute the slope [tex]\(m = 6\)[/tex]:
[tex]\[ y - y_1 = 6(x - x_1) \][/tex]
3. Substitute the point [tex]\((x_1, y_1) = (1, 2)\)[/tex]:
[tex]\[ y - 2 = 6(x - 1) \][/tex]
Simplifying, we get the equation:
[tex]\[ y - 2 = 6(x - 1) \][/tex]
Thus, the point-slope form of the line with slope [tex]\(6\)[/tex] passing through the point [tex]\((1, 2)\)[/tex] is:
[tex]\[ y - 2 = 6(x - 1) \][/tex]
So, the correct option is:
A. [tex]\( y - 2 = 6(x - 1) \)[/tex]
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
where [tex]\((x_1, y_1)\)[/tex] is a given point on the line and [tex]\(m\)[/tex] is the slope.
Given the slope [tex]\(m = 6\)[/tex] and the point [tex]\((1, 2)\)[/tex], we can substitute these values into the formula:
1. Start with the point-slope formula:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
2. Substitute the slope [tex]\(m = 6\)[/tex]:
[tex]\[ y - y_1 = 6(x - x_1) \][/tex]
3. Substitute the point [tex]\((x_1, y_1) = (1, 2)\)[/tex]:
[tex]\[ y - 2 = 6(x - 1) \][/tex]
Simplifying, we get the equation:
[tex]\[ y - 2 = 6(x - 1) \][/tex]
Thus, the point-slope form of the line with slope [tex]\(6\)[/tex] passing through the point [tex]\((1, 2)\)[/tex] is:
[tex]\[ y - 2 = 6(x - 1) \][/tex]
So, the correct option is:
A. [tex]\( y - 2 = 6(x - 1) \)[/tex]
