Write an equation of the line that is:

a) Parallel to the line [tex]y = 4x + 1[/tex] and passes through the point (2, 3).

b) Parallel to the line [tex]2y - 6x = 9[/tex] and passes through the point (-2, 1).

c) Parallel to the line [tex]y = 4x + 3[/tex] and has the same y-intercept as the line [tex]y = 5x - 3[/tex].

d) Parallel to the line [tex]y = -\frac{1}{2}x[/tex] and has the same y-intercept as the line [tex]2y = 7x + 6[/tex].

e) Perpendicular to the line [tex]2y - 4x = 8[/tex] and passes through the point (6, -6).

f) Perpendicular to the line [tex]2y - 5x = 15[/tex] and has an x-intercept of 3.

a ) y = 4 x + 1 a = 4 n e w y = b x + c i f p a r a ll e l a = b y = 4 x + c s u b s t i t u t in g \point ( 2 , 3 ) 3 = 4 ∗ 2 + c c = − 5 y = 4 x − 5 b ) 2 y − 6 x = 9 2 y = 6 x + 9 y = 3 x + 4 , 5 a = 3 n e w y = b x + c i f p a r a ll e l a = b y = 3 x + c s u b s t i t u t in g p o in t ( − 2 , 1 ) 1 = 4 ∗ ( − 2 ) + c c = 9 y = 3 x + 9 c ) y = 4 x + 3 a = 4 n e w y = b x + c i f p a r a ll e l a = b y = 4 x + c c = − 3 y = 4 x − 3 e ) 2 y − 4 x = 8 2 y = 4 x + 8 y = 2 x + 4 a = 2 n e w \y = b x + c i f p er p e n d i c u l a r b = − 1/ a y = − 2 1 ​ x + c p o in t ( 6 , − 6 ) − 6 = − 1/2 ∗ 6 + c c = − 3 y = − 1/2 x − 3 f ) 2 y − 5 x = 15 2 y = 5 x + 15 y = 2 5 ​ x + 2 15 ​

Answered by luana | 2024-06-10

The problem consists of finding equations of lines either parallel or perpendicular to given lines and passing through specified points. Detailed steps for each part show how to determine slopes, y-intercepts, and form final equations. The answers include: y = 4 x − 5 , y = 3 x + 7 , y = 4 x − 3 , y = − 2 1 ​ x + 3 , y = − 2 1 ​ x − 3 , and y = − 5 2 ​ x + 5 6 ​ .
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Answered by luana | 2025-06-15