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Suppose you graphed every single point of the form $$(2t + 3, 3-3t)$$. For example, when t=2, we have 2t + 3 = 7 and 3-3t = -3, so (7,-3) is on the graph. Explain why the graph is a line, and find an equation whose graph is this line.

In order for this graph to be a line, we need to verify two things: first, that all the points on the graph are on the proposed line and second, that all points on the proposed line are on the graph. Be sure to deal with both.

Guest Mar 7, 2018

#1
+68
+1

Since the graph is a line, it's easy to solve for two points on a graph, draw a line, and figure out what the equation is. You've already got one point, so now you need a second one. I'm going to use t=1 just so I can get points that are right next to each other.

$$(2t+3, 3-3t)$$

$$(2+3, 3-3)$$

$$(5, 0)$$

Now we need to put these two points on a graph.

Connect the lines and extend out until you hit the edges of the graph.

After this, you need to figure out $$y = ax+b$$, where a is $$\frac{rise}{run}$$ and b is where the point crosses the y-axis.

For x, if we zoom in, we can see that it goes down 3 and to the right 2 every time it tries to get to a new point.

If we follow $$\frac{rise}{run}$$ , a should be $$\frac{-3}{2}$$

B is the y-intercent (or where the line crosses the y-axis). That number is 7.5, so b is 7.5.

The final answer for the graph should be $$y=-\frac{3}{2}t+7.5$$.

CoopTheDupe  Mar 7, 2018
#1
+68
+1

Since the graph is a line, it's easy to solve for two points on a graph, draw a line, and figure out what the equation is. You've already got one point, so now you need a second one. I'm going to use t=1 just so I can get points that are right next to each other.

$$(2t+3, 3-3t)$$

$$(2+3, 3-3)$$

$$(5, 0)$$

Now we need to put these two points on a graph.

Connect the lines and extend out until you hit the edges of the graph.

After this, you need to figure out $$y = ax+b$$, where a is $$\frac{rise}{run}$$ and b is where the point crosses the y-axis.

For x, if we zoom in, we can see that it goes down 3 and to the right 2 every time it tries to get to a new point.

If we follow $$\frac{rise}{run}$$ , a should be $$\frac{-3}{2}$$

B is the y-intercent (or where the line crosses the y-axis). That number is 7.5, so b is 7.5.

The final answer for the graph should be $$y=-\frac{3}{2}t+7.5$$.

CoopTheDupe  Mar 7, 2018