Write an equation in slope-intercept form of the line with the given parametric equations,
x = 8t+3
y= 9t+3

The equation in slope-intercept from is y = .

Step-by-step explanation:

Given,

x = 8t+3

y= 9t+3

First, convert both the equations in terms of t for comparison.

x = 8t + 3

x - 3 = 8t

t =

Similarly,

y = 9t + 3

y - 3 = 9t

t =

Now, comparing both equations

=  

9x -27 = 8y -24

9x - 3 = 8y

or

y =

Hence, the equation in slope-intercept from is y = .

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is