Question

consider the following parametric equations:

$x = \frac{4t - 15}{2}$ and $y = 3 - t$

step 2 of 2 : plot the points that result from the integer $t$-values from zero to five on the graph. round the $x$- and $y$-coordinates of each point to one decimal place, if necessary.

Explanation:

Step1: Find \(x\) and \(y\) for \(t = 0\)

Substitute \(t=0\) into \(x=\frac{4t - 15}{2}\) and \(y = 3-t\).
For \(x\): \(x=\frac{4\times0-15}{2}=\frac{- 15}{2}=-7.5\)
For \(y\): \(y=3 - 0=3\)

Step2: Find \(x\) and \(y\) for \(t = 1\)

Substitute \(t = 1\) into \(x=\frac{4t - 15}{2}\) and \(y = 3-t\).
For \(x\): \(x=\frac{4\times1-15}{2}=\frac{4 - 15}{2}=\frac{-11}{2}=-5.5\)
For \(y\): \(y=3-1 = 2\)

Step3: Find \(x\) and \(y\) for \(t = 2\)

Substitute \(t = 2\) into \(x=\frac{4t - 15}{2}\) and \(y = 3-t\).
For \(x\): \(x=\frac{4\times2-15}{2}=\frac{8 - 15}{2}=\frac{-7}{2}=-3.5\)
For \(y\): \(y=3 - 2=1\)

Step4: Find \(x\) and \(y\) for \(t = 3\)

Substitute \(t = 3\) into \(x=\frac{4t - 15}{2}\) and \(y = 3-t\).
For \(x\): \(x=\frac{4\times3-15}{2}=\frac{12-15}{2}=\frac{-3}{2}=-1.5\)
For \(y\): \(y=3 - 3=0\)

Step5: Find \(x\) and \(y\) for \(t = 4\)

Substitute \(t = 4\) into \(x=\frac{4t - 15}{2}\) and \(y = 3-t\).
For \(x\): \(x=\frac{4\times4-15}{2}=\frac{16 - 15}{2}=0.5\)
For \(y\): \(y=3 - 4=-1\)

Step6: Find \(x\) and \(y\) for \(t = 5\)

Substitute \(t = 5\) into \(x=\frac{4t - 15}{2}\) and \(y = 3-t\).
For \(x\): \(x=\frac{4\times5-15}{2}=\frac{20 - 15}{2}=2.5\)
For \(y\): \(y=3 - 5=-2\)

Answer:

The points are \((-7.5,3)\), \((-5.5,2)\), \((-3.5,1)\), \((-1.5,0)\), \((0.5,-1)\), \((2.5,-2)\)