Question

2x + 3y = 18 3x -4y > 16. Give the Domain and Range, Slope, and Y-intercept for each line. Graph each equation above on the graph below and show all work. Give the Domain and Range, Slope, and Y-intercept for each line. Explain in detail how you got each answer. 2x + 3y = 18 3x -4y > 16 Slope-Intercept Form: Slope-Intercept Form: Domain: Domain: Range: Range: Slope: Slope: Y-intercept: Y-intercept:

Answer 1

we have that
2x + 3y = 18
3x -4y > 16

Part A)
2x + 3y = 18 -------> 3y=[18-2x]---------> y=6-(2/3)x (Slope-Intercept Form)

using a graph tool
see the attached figure

the domain is the interval (-∞,∞)--------> ( all real numbers)
Domain of a function f (x) is the set of all the values ​​of x for which the function is defined

the range is the interval (-∞,∞)--------> ( all real numbers)
Range of the function f(x) is the set of all the values ​​that f(x) takes

Slope-Intercept Form------------> y=6-(2/3)x---------> [y=mx+b]
where
m------> is the slope------------> m=-2/3
Slope=-2/3
Y-intercept is the point for y=0
y=6-(2/3)x-------------> 0=6-(2/3)x--------> x=9
Y-intercept is the point (9,0)

Part B)
3x -4y > 16----------> -4y > 16-3x-----> y < -4+(3/4)x (Slope-Intercept Form)
using a graph tool
see the attached figure

the domain is the interval (-∞,∞)--------> ( all real numbers)
Domain of a function f (x) is the set of all the values ​​for which the function is defined

the range is the interval (-∞,∞)--------> ( all real numbers)
Range of the function f(x) is the set of all the values ​​that f(x) takes

Slope-Intercept Form------------> y = -4+(3/4)x---------> [y=mx+b]
where
m------> is the slope------------> m=3/4
Slope=3/4
Y-intercept is the point for y=0
y = -4+(3/4)x------------->0= -4+(3/4)x-----> 4=(3/4)x----> 16/3 = x----> x=16/3
Y-intercept is the point (5.33,0)