Respuesta :
Answer:
k = [tex]\frac{15}{4}[/tex]
Step-by-step explanation:
Parallel lines have equal slopes.
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange both equations into this form and equate slopes
2x + 5y = 1 ( subtract 2x from both sides )
5y = - 2x + 1 ( divide all terms by 5 )
y = - [tex]\frac{2}{5}[/tex] x + [tex]\frac{1}{5}[/tex] ← in slope- intercept form
with slope m = - [tex]\frac{2}{5}[/tex]
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3x + 2ky = 2 ( subtract 3x from both sides )
2ky = - 3x + 2 ( divide all terms by 2k )
y = - [tex]\frac{3}{2k}[/tex] x + [tex]\frac{2}{2k}[/tex] ← in slope- intercept form
with slope m = - [tex]\frac{3}{2k}[/tex]
Thus
- [tex]\frac{2}{5}[/tex] = - [tex]\frac{3}{2k}[/tex] ( multiply both sides by - 1 )
[tex]\frac{2}{5}[/tex] = [tex]\frac{3}{2k}[/tex] ( cross- multiply )
4k = 15 ( divide both sides by 4 )
k = [tex]\frac{15}{4}[/tex]
Answer:
k = 3.75.
Step-by-step explanation:
Convert each equation to slope-intercept form.
2x + 5y = 1
5y = -2x + 1
y = -0.4x + 0.2.
3x + 2ky = 2
2ky = -3x + 2
y = (-1/5/k) x + 2/2k
y = (--1.5/k)x + 1/k.
If they are parallel then -1.5 / k =-0.4
k = -1.5 / -0.4
So k = 3.75
