Question

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

Answer 1

Answer:

4/6

Step-by-step explanation:

14-10

--------   = 4/6

12-6

Answer 2

Answer:

The point-slope form an equation for the line through the points (6, 10) and (12, 14) is $y=\frac{2}{3} x+6$

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

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$   --- eqn 2

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

Hence we get $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

By substituting the values in equation (2),

$m=\frac{14-10}{12-6}$

On simplifying above term,

$m=\frac{4}{6}=\frac{2}{3}$

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

$y=\frac{2}{3} x+c$   --- 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).

$10=\frac{2}{3}(6)+c$

10=4+c

c=6

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

$y=\frac{2}{3} x+6$

Hence point-slope form an equation for the line through the points (6, 10) and (12, 14) is $y=\frac{2}{3} x+6$