What is the equation of the line that is perpendicular to the given line and passes through the point (3, 0)? 3x + 5y = −9 3x + 5y = 9 5x − 3y = −15 5x − 3y = 15

5x - 3y = 15

Step-by-step explanation:

3x + 5y = −9 can be solved for y (and thus for the slope explicitly):

5y = -3x - 9, or y = (-3/5)x - 9/5.  The slope of the given line is -3/5.  The slope of a line perpendicular to the given line is the negative reciprocal of this -3/5, which is 5/3.  Substituting 3 for x and 0 for y, our slope-intercept  equation y = mx + b becomes 0 = (5/3)(3) + b, which leads to b = -5:

y = (5/3)x - 5.  We must put this back into standard form, starting by multiplying all three terms by 3:

3y = 5x - 15, or -5x + 3y = -15.  This is equivalent to 5x - 3y = 15 (which is the last answer choice).

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

step-by-step explanation: