Write an equation of the line passing through point P(3,8) that is parallel to the line y
= 1/5 (x+4)

Answer:

y=1/5(x+37)

Step-by-step explanation:

y=1/5x+4/5

Plug in the (3,8)

8=1/5(3)+b

8=3/5+b

7 2/5=b

y=1/5(x+37)

The equation of the line is y = 1/5(x + 37)

Since our new line is parallel to the line y = 1/5(x + 4), and 1/5 is the gradient of the line y = 1/5(x + 4), the gradient of the new line is 1/5.

Using the equation of a line in slope-point form,  [tex]\frac{y - y_{1} }{x - x_{1} } = m[/tex] where (x₁, y₁) = (3, 8) and m = 1/5

Substituting the values of the variables into the equation, we have

[tex]\frac{y - y_{1} }{x - x_{1} } = m[/tex]

[tex]\frac{y - 8 }{x - 3 } = \frac{1}{5}[/tex]

Cross-multiplying. we have

5(y - 8) = x - 3

Expanding the bracket, we have

5y - 40 = x - 3

5y = x - 3 + 40

5y = x + 37

y = 1/5(x + 37)

So, the equation of the line is y = 1/5(x + 37)

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