y = - [tex]\frac{2}{5}[/tex] 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 = - [tex]\frac{2}{5}[/tex] x + 2 ← point- slope form with slope m = - [tex]\frac{2}{5}[/tex]
Parallel lines have equal slopes hence
y = - [tex]\frac{2}{5}[/tex] 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 = - [tex]\frac{2}{5}[/tex] x - 2 ← equation of parallel line
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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