What is the equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10? enter your answer in the box

The equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10 is; 5y + 2x = -10

According to the question, we are required to determine the equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10

The equation of the line 2x + 5y = 10 when rewritten in the slope-intercept, y = (-2/5)x + 2 is;

However, parallel lines have equal slope;

The equation of the line which passes through the point (5, -4) is;

Slope, m =

By cross product;

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y = - x - 2

the equation of a line in slope- intercept form is

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

rearrange 2x + 5y = 10 into this form

subtract 2x from both sides

5y = - 2x + 10 ( divide all terms by 5 )

y = - x + 2 ← point- slope form with slope m = -

Parallel lines have equal slopes hence

y = - x + c is the partial equation of the parallel line

to find c, substitute ( 5, - 4 ) into the partial equation

- 4 = - 2 + c ⇒ c = - 4 + 2 = - 2

y = - x - 2 ← equation of parallel line