A line passes through the points (16, c) and (18, 23) and has a slope of 2/3 . find the value of c.
Answers
Answer:
c = 65/3
Step-by-step explanation:
The general (slope intercept form) equation for any line is y=mx+b. Where m represents the slope and b represents the y-intercept. I am going to use the known slope of the line and one of the points (18,23) to create the equation for the line.
Substitue m for 2/3, y for 23, and x for 18.
23=(2/3)18+b
Solve for b and we get b= 11.
Now we have our equation for this line, y= (2/3)x +11
In order to find the missing y-coordinate in the point (16,c), we use our equation of this line to see what happens to the y-coordinate when x=16.
Using our equation: y= (2/3)x +11. Substitue x for 16.. y= (2/3)16 +11
Simplify the right side of our equation and we get y = 65/3
This tells us the corresponding y-coordinate is 65/3. Thus c=65/3