Find the equation of a line parallel to 2x-3y=9 that passes through the point (1, -3)

y = 2/3x - 11/3

Step-by-step explanation:

2x-3y=9

Rearrange to find the parallel gradient:

-3y = -2x+9

y = 2/3x -3

M(gradient) = 2/3

M(parallel gradient) = 2/3

Substitute the gradient and the points point A and B into the equation :

y-b = m(x-a)

y - (-3) = 2/3(x-1)

3y + 9 = 2x -2

3y = 2x -11

y = 2/3x - 11/3

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true