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line m passes through point (-2,-1) and is perpendicular to the graph of y=-2/3x+6. Line n is parallel to line m and passes through the point (4,-3).What is the equation in slope-intercept form of the line n?

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dhiab

Answer:

Hello...... here is a solution :

1 -  

Hello:

the   equation of "m" is : y = ax+b

the slope is a : a×(- 2/3) = -1......( perpendicular to a line : y=-2/3x+6 when the slope is -2/3 )

a = 3/2          

the line " n" that passes through (4, - 3) and  parallel to line "m" :  

when the slope is 3/2 ( same slope )

the equation in slope-intercept form of the line" n" is :

 y – (-3)= (3/2)(x – 4)







tramserran

Answer: [tex]\bold{y=\dfrac{3}{2}x-9}[/tex]

Step-by-step explanation:

Line m is perpendicular to [tex]y=-\dfrac{2}{3}x+6[/tex]. Perpendicular means opposite and reciprocal slope, so

[tex]m=-\dfrac{2}{3}\ \quad m_\perp=\dfrac{3}{2}[/tex]

Line n is parallel to Line m. Parallel means same slope, so [tex]m=\dfrac{3}{2}[/tex]


Next, input the point (4, -3) and the slope [tex]\bigg(\dfrac{3}{2}\bigg)[/tex] into the Point-Slope formula: y- y₁ = m(x - x₁)

[tex]y - (-3) = \dfrac{3}{2}(x-4)[/tex]


Now, rewrite the equation in Slope-Intercept form - distribute the slope and solve for "y".

[tex]y + 3 = \dfrac{3}{2}x-\dfrac{3}{2}(4)[/tex]

[tex]y + 3 = \dfrac{3}{2}x-6[/tex]

   [tex]y = \dfrac{3}{2}x-9[/tex]




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