Question

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

Answer 1

Answer:

The Equation of line with points (4 , - 3) and slope $\dfrac{3}{2}$ is y =  $\dfrac{3}{2}$ x - 9

Step-by-step explanation:

Given equation of line as :

 y = $\dfrac{-2}{3}$x + 6

∵ Standard equation of line is give as

y = a x + c

Where m is the slope of line and c is the y-intercept

Now, comparing given line equation with standard eq

So, The slope of the given line = a = $\dfrac{-2}{3}$

Again,

The other line if passing through the points (- 2 , - 1 ) And  is perpendicular to given line

So, for perpendicular lines condition , the products of slope of both lines = - 1

Let The slope of other line = m

So,  m × a = - 1

Or, m × $\dfrac{-2}{3}$ = - 1

So, m = $\dfrac{- 1}{\frac{ -2 }{3}}$

∴ m = $\dfrac{3}{2}$

Now, Again

The line n is parallel to the line m and passes through the points (4 , - 3)

∵ Line n parallel to line m so, The slope of both are equal

Let The slope of line n is M

So, M = m =  $\dfrac{3}{2}$

So, The equation of line written as

y = M x + c

Or, - 3 =  $\dfrac{3}{2}$ ( 4 ) + c

Or, - 3 = $\frac{3\times 4}{2}$ + c

Or, - 3 = 6 + c

Or, c = - 3 - 6

∴ c = - 9

So, Equation of line with points (4 , - 3) and slope $\dfrac{3}{2}$ is

y =  $\dfrac{3}{2}$ x - 9

Hence , The Equation of line with points (4 , - 3) and slope $\dfrac{3}{2}$ is y =  $\dfrac{3}{2}$ x - 9    Answer