Question

Find an equation of the line such that the points (2/5,5) and (-2/5,4) are on the line.

Answer 1

The equation of the line is y = $\frac{5}{4}$ x +  $\frac{9}{2}$

Step-by-step explanation:

The form of the linear equation is y = mx + b, where

• m is the slope of the line, $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$
• b is the y-intercept, to find b substitute x and y in the equation by the coordinates of any point on the line

∵ A line passes through points ( $\frac{2}{5}$ , 5) and ( $-\frac{2}{5}$ , 4)

∴ $x_{1}$ =  $\frac{2}{5}$  and $x_{2}$  =  $-\frac{2}{5}$

∴ $y_{1}$ = 5  and  $y_{2}$ = 4

- Substitute them in the rule of the slope to find m

∵ $m=\frac{4-5}{-\frac{2}{5}-\frac{2}{5} }$

∴ $m=\frac{-1}{-\frac{4}{5}}=\frac{5}{4}$

- Substitute it in the form of the equation

∴ y = $\frac{5}{4}$ x + b

- To find b substitute x and y in the equation by the coordinates

   of any point on the line

∵ Point ( $\frac{2}{5}$ , 5) lies on the line

∴ x = $\frac{2}{5}$  and y = 5

∴ 5 = $\frac{5}{4}$ (  $\frac{2}{5}$ ) + b

∴ 5 = $\frac{1}{2}$ + b

- Subtract  $\frac{1}{2}$  from both sides

∴ $\frac{9}{2}$  = b

∴ y = $\frac{5}{4}$ x +  $\frac{9}{2}$

The equation of the line is y = $\frac{5}{4}$ x +  $\frac{9}{2}$

Learn more:

You can learn more about the linear equations in brainly.com/question/1284310

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