Question

X = 2t
y = t + 5, -2 ≤ t ≤ 3
Can you please graph this

Answer 1

The answer is in attachment

Explanation:

First step finde a function t(x) ⇒ t=x/2;

Now we need to finde the limits of that function:

if t=-2 ⇒ x=-4 and t=3 ⇒ x=6. That means -4≤x≤6

Now replace on y(t) ⇒ y(x)= x/2+5, 4≤x≤6

Answer 2

See attachment

Explanation:

The given parametric equations are;

`x=2t` and
`y=t+5`,
`-2\le t\le 3`.

We can graph this by plotting some few points within the given range or eliminate the parameter to identify the type of curve.

Plotting points;

When
`t=-2`,

`x=2(-2)=4` and
`y=-2+5=3`

This gives the point (-4,3).

When
`t=0`

`x=2(0)=0` and
`y=0+5=5`

This gives the point (0,5).

When
`t=3`

`x=2(3)=6` and
`y=3+5=8`

This gives the point (6,8).

We plot these points and draw a straight line through them.

Eliminating the parameter.

`x=2t`

`y=t+5`

Make t the subject in the second equation;

`t=y-5`

Substitute into the first equation;

`x=2(y-5)`

This implies that;

`x=2y-10`

`y=(1)/(2)x+5`

This is an equation of a straight line with slope
`(1)/(2)` and y-intercept 5 on the interval

`-4\le x \le 6`