Question

Find the slope of the line joining the points (2,2) (5,3).Find its equation of line​

Answer 1

Answer:

slope,m= 3-2/ 5-2

m= 1/3

therefore equation of line is( y- 2)= 1/3 ( x- 2)

3y - 6 = X - 2

X - 3y +4 = 0

Answer 2

Answer:

1. Slope of the line = $\frac{1}{3}$
2. Equation of the line  is x - 3y +4 = 0

Step-by-step explanation:

Given,

An line passing through the points (2,2) (5,3)

To find,

1. Slope of the line
2. Equation of the line

Recall the formulas

1. The slope of the line (m) passing through the point $(x_1,y_1)$  and $(x_2,y_2)$ is given by the formula, m = $\frac{y_2 - y_1}{x_2 - x_1}$
2. Equation of the line with slope 'm' and passing through the point   $(x_1,y_1)$ is given by the formula,  $y - y_1 = m(x-x_1)$

Solution:

We have, $(x_1,y_1)$ = (2,2) and $(x_2,y_2)$ = (5,3)

To find slope

Substituting the values of $x_1,x_2,y_1 \ and\ y_2$ in formula (1) we get

m = $\frac{y_2 - y_1}{x_2 - x_1}$ = $\frac{3- 2}{5 -2} = \frac{1}{3}$

∴ Slope of the line = $\frac{1}{3}$

To find the equation of the line

Substituting the value of 'm' and $(x_1,y_1)$ in formula (2) we get

y - 2 = $\frac{1}{3}$ ( x-2)

3(y-2) = x-2

3y - 6 = x -2

x - 3y +4 = 0

Hence, equation of the line  is x - 3y +4 = 0

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