Question

Set up a table of values and then graph the line from its parametric form. x=-3t +4 y= 2t-5

Answer 1

y =
`(2)/(3)` x -
`(7)/(3)`

Explanation:

Given

• x=-3t + 4

So we will set up a set values of t to have x

t = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

<=> x = {4, 1, -2, -5, -8, -11, -14, -17, -20, -23, -26}

• y= 2t-5

So we will set up a set values of t to have y

t = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

<=.> y = {-5, -3, -1, 1, 3, 5, 7, 9, 11, 13, 15}

At the end, we have the table of values of x and y as following:

x = {4, 1, -2, -5, -8, -11, -14, -17, -20, -23, -26}

y = {-5, -3, -1, 1, 3, 5, 7, 9, 11, 13, 15}

Let find the slope of the linear equation:

m =
`(y2-y1)/(x2-x1)`

<=> m =
`(-3-(-5))/(1-4)` =
`-(2)/(3)`

and the standard form of a linear equation is:

y= mx + b

In this situation, y =
`(2)/(3)` x + b (1)

Because the line goes through point (4, -5), so we substitute it into (1) to find b.

<=> -5 =
`-(2)/(3)`*4 + b

<=> b = -
`(23)/(3)`

<=> y =
`(2)/(3)` x -
`(7)/(3)`

Please have a look at the attach photo.

Hope it will find you well.