Question

1. Use the given conditions to write an equation for the line in​ point-slope form and general form. Passing through (−4,4) and parallel to the line whose equation is 7x−9y−8=0 Question content area bottom Part 1 The equation of the line in​ point-slope form is enter your response here. ​(Type an equation. Use integers or fractions for any numbers in the​ equation.) Part 2 The equation of the line in general form is enter your response here=0. ​(Type an expression using x and y as the variables. Simplify your answer. Use integers or fractions for any numbers in the​ expression.)

Answer 1

1) The equation of the line passing through (−4, 4) and parallel to the line whose equation is 7x − 9y − 8 = 0 is; y - 4 =  ⁷/₉(x + 4)

How to find the equation of a line?

1) We are told that the line passes through (−4, 4) and is parallel to the line whose equation is 7x − 9y − 8 = 0

Thus, let us rearrange to find the slope.

7x − 9y − 8 = 0

⇒ 9y = 7x - 8

⇒ y = ⁷/₉x - ⁸/₉

Slope; m = ⁷/₉

Now,  the point slope formula is;

y − y₁ = m(x − x₁)

where;

y₁ is the y-coordinate

x₁ is the x-coordinate

m is the slope

Thus the line Passing through (−4,4) is;

y - 4 =  ⁷/₉(x + 4)

2) The equation in general form is;

y = 4 + ⁷/₉x + ²⁸/₉

y = ⁷/₉x + ⁶⁴/₉

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