Find the equation of the line passing through the two points (2,8),(6,1)
To find the equation of the line passing through the points (2,8) and (6,1), follow the steps below:
- Step 1: Calculate the slope m.
The formula for the slope m is:
m=x2āāx1āy2āāy1āā=6ā21ā8ā=4ā7ā
- Step 2: Use the point-slope form to write the equation of the line.
The point-slope form of a line is given by:
yāy1ā=m(xāx1ā)
Using the point (2,8):
yā8=ā47ā(xā2)
- Step 3: Simplify to the slope-intercept form.
Distribute the slope and rearrange to find y:
yā8=ā47āx+27ā
Add 8 to both sides to solve for y:
y=ā47āx+27ā+8
Convert 8 to a fraction with a denominator of 2:
y=ā47āx+27ā+216ā
Simplify the addition:
y=ā47āx+223ā
To convert 23/2 into mixed number form: 223ā=1121ā
Thus, the equation in slope-intercept form is: y=ā47āx+1121ā
Therefore, the equation of the line passing through these points is y=ā143āx+1121ā, which matches the correct choice in the multiple-choice answers.
y=ā143āx+1121ā