Question

Write in point-slope form an equation for the line through the points (6, 10) and (12, 14).

Answer 1

4/6

Explanation:

14-10

-------- = 4/6

12-6

Answer 2

The point-slope form an equation for the line through the points (6, 10) and (12, 14) is
`y=(2)/(3) x+6`

Solution:

The slope - intercept form equation of line is given as

y=mx+c --- eqn (1)

Where m is the slope of the line. The coefficient of “x” is the value of slope of the line.

Where slope of the line which is passes through
`\left(\mathrm{x}_(1), \mathrm{y}_(1)\right) and \left(\mathrm{x}_(2), \mathrm{y}_(2)\right)` is given as

`m=(y_(2)-y_(1))/(x_(2)-x_(1))` --- eqn 2

From question given that two points are (6, 10), (12,14).

Hence we get
`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

By substituting the values in equation (2),

`m=(14-10)/(12-6)`

On simplifying above term,

`m=(4)/(6)=(2)/(3)`

On substituting the value of m in equation (1),

`y=(2)/(3) x+c` --- eqn 3

Now equation (3) passes through given two points that is (6, 10), (12,14), so on substituting x = 6 and y=10 in equation (3).

`10=(2)/(3)(6)+c`

10=4+c

c=6

Now on substituting the value of c = 6 in equation (3),

`y=(2)/(3) x+6`

Hence point-slope form an equation for the line through the points (6, 10) and (12, 14) is
`y=(2)/(3) x+6`