The equation of the line is y = [tex]\frac{5}{4}[/tex] x + [tex]\frac{9}{2}[/tex]
Step-by-step explanation:
The form of the linear equation is y = mx + b, where
∵ A line passes through points ( [tex]\frac{2}{5}[/tex] , 5) and ( [tex]-\frac{2}{5}[/tex] , 4)
∴ [tex]x_{1}[/tex] = [tex]\frac{2}{5}[/tex] and [tex]x_{2}[/tex] = [tex]-\frac{2}{5}[/tex]
∴ [tex]y_{1}[/tex] = 5 and [tex]y_{2}[/tex] = 4
- Substitute them in the rule of the slope to find m
∵ [tex]m=\frac{4-5}{-\frac{2}{5}-\frac{2}{5} }[/tex]
∴ [tex]m=\frac{-1}{-\frac{4}{5}}=\frac{5}{4}[/tex]
- Substitute it in the form of the equation
∴ y = [tex]\frac{5}{4}[/tex] x + b
- To find b substitute x and y in the equation by the coordinates
of any point on the line
∵ Point ( [tex]\frac{2}{5}[/tex] , 5) lies on the line
∴ x = [tex]\frac{2}{5}[/tex] and y = 5
∴ 5 = [tex]\frac{5}{4}[/tex] ( [tex]\frac{2}{5}[/tex] ) + b
∴ 5 = [tex]\frac{1}{2}[/tex] + b
- Subtract [tex]\frac{1}{2}[/tex] from both sides
∴ [tex]\frac{9}{2}[/tex] = b
∴ y = [tex]\frac{5}{4}[/tex] x + [tex]\frac{9}{2}[/tex]
The equation of the line is y = [tex]\frac{5}{4}[/tex] x + [tex]\frac{9}{2}[/tex]
Learn more:
You can learn more about the linear equations in brainly.com/question/1284310
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