To find the equation of a line passing through the points [tex]\( (4, 17) \)[/tex] and [tex]\( (1, 11) \)[/tex], we need to follow these steps:
1. Calculate the slope of the line (m):
The formula for the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Substituting the given points [tex]\((4, 17)\)[/tex] and [tex]\((1, 11)\)[/tex]:
[tex]\[
m = \frac{11 - 17}{1 - 4} = \frac{-6}{-3} = 2.0
\][/tex]
So, the slope [tex]\(m\)[/tex] is [tex]\(2.0\)[/tex].
2. Find the line's equation in point-slope form using the point (4, 17):
The point-slope form of a line's equation is:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
Using the point [tex]\((4, 17)\)[/tex]:
[tex]\[
y - 17 = 2.0(x - 4)
\][/tex]
3. Find the line's equation in point-slope form using the point (1, 11):
Again, using the point-slope form:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
Using the point [tex]\((1, 11)\)[/tex]:
[tex]\[
y - 11 = 2.0(x - 1)
\][/tex]
So, the equations in point-slope form are:
- Using the point [tex]\((4, 17)\)[/tex]: [tex]\( y - 17 = 2.0(x - 4) \)[/tex]
- Using the point [tex]\((1, 11)\)[/tex]: [tex]\( y - 11 = 2.0(x - 1) \)[/tex]
