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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