(-8,2); 5x-4y=4. write an equation through the point and parallel to the given line

The equation passing through the point (-8, 2) and parallel to 5x - 4y = 4 is

y   =  5/4 x   +  12

The given equation is:

5x   -  4y   =   4

Rewrite the equation 5x   -  4y   =   4 in the form y = mx + c

4y  =   5x  -  4

y   =  5/4 x  -  4/4

y   =  5/4 x  -  1

where the slope, m = 5/4 and the intercept, c = -1

The equation of a line is of the form:

y - y₁   =  m(x  -  x₁)

The line passes through the point (-8, 2)

That is,  x₁  =  -8,  y₁  =  2

Substitute x₁ = -8 and y₁ = 2 into the equation y - y₁  =  m(x  - x₁)

y   -  2   =  5/4 (  x   -  -8)

y  -  2  =  5/4 (x  +  8)

y   =  5/4 x  +  8(5/4)  +  2

y   =  5/4 x  +  10   +  2

y   =  5/4 x   +  12

The equation passing through the point (-8, 2) and parallel to 5x - 4y = 4 is

y   =  5/4 x   +  12

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y = x + 12

Step-by-step explanation:

the equation of a line in slope-intercept form is

y = mx + c ( m is the slope and c the y-intercept )

rearrange 5x - 4y = 4 into this form

subtract 5x from both sides

- 4y = - 5x + 4 ( divide all terms by - 4 )

y = x - 1 ← in slope-intercept form

with slope m =

• Parallel lines have equal slopes, hence

y = x + c ← is the partial equation

to find c substitute (- 8, 2 ) into the partial equation

2 = - 10 + c ⇒ c = 2 + 10 = 12

y = x + 12 ← equation of parallel line