Question

What is an equation of the line that passes through the point (-5,2) and is parallel
to the line 4x - 5y = 5?

Answer 1

Answer:

Step-by-step explanation:

first change the equation so it just equals y

-5y = 5 -4x

y = 4/5x -1

since this new equation has to be parallel to the previous line, the slopes are the same

y = 4/5x + b

now we have to make sure the new equation passes through (-5,2) so we plug in -5 for x and 2 for y

2 = 4/5(-5) + b

2 = -4 + b

b = 6

so the final equation is

y = 4/5x +6

Answer 2

The equation of the line that passes through the point (-5,2) and is parallel  to the line 4x - 5y = 5 is 5y - 4x = 30

The equation of a line in point-slope form is expressed as:

$y-y_0=m(x-x_0)$

m is the slope of the line

(x0, y0) is any point on the line

Given the equation 4x - 5y = 5.

Rewrite in standard form:

-5y = -4x + 5

y = 4/5 x - 1

The slope of the line passing through the given equation is 4/5

Substitute the slope and the point into the equation:

$y-2=4/5(x+5)\\5(y-2)=4(x+5)\\5y-10=4x+20\\5y-4x=20+10\\5y-4x=30$

Hence the equation of the line that passes through the point (-5,2) and is parallel  to the line 4x - 5y = 5 is 5y - 4x = 30

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