Question

Write an equation of the line passing through the point (5, 8)​ that is parallel to the line 7x+5y=3​

Answer 1

y = (-7/5) x + 15

Explanation:

Let's name the line whose formula we'll calculate as line A. The other line is line B.

Rewrite the equation of line B:

• 7x+5y=3​

• y = -7x/5 + 3/5

A parallel line has to have the same slope (-7/5). With that information in mind, we only need to calculate b (following the basic equation for a line, y=mx+b).

Line A passes through the point (5,8), so we can express the slope as:

• m =
  `(y_2-y_1)/(x_2-x_1)=(8-y_1)/(5-0) =-(7)/(5)`

So we solve for y₁:

• 8-y₁ = -7

• y₁ = 15

That is the value in the Y-axis line A crosses when x=0. In other words, it is b.

The equation is y = (-7/5) x + 15