Question

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?

Answer 1

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)

Answer 2

Answer: $\bold{y=\dfrac{3}{2}x-9}$

Step-by-step explanation:

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

$m=-\dfrac{2}{3}\ \quad m_\perp=\dfrac{3}{2}$

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

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

$y - (-3) = \dfrac{3}{2}(x-4)$

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

$y + 3 = \dfrac{3}{2}x-\dfrac{3}{2}(4)$

$y + 3 = \dfrac{3}{2}x-6$

   $y = \dfrac{3}{2}x-9$