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

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=(3)/(2)x-9}`

Explanation:

Line m is perpendicular to
`y=-(2)/(3)x+6`. Perpendicular means opposite and reciprocal slope, so

`m=-(2)/(3)\ \quad m_\perp=(3)/(2)`

Line n is parallel to Line m. Parallel means same slope, so
`m=(3)/(2)`

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

`y - (-3) = (3)/(2)(x-4)`

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

`y + 3 = (3)/(2)x-(3)/(2)(4)`

`y + 3 = (3)/(2)x-6`

`y = (3)/(2)x-9`