Lesson 12
Using Equations for Lines
Let’s write equations for lines.
Problem 1
Select all the points that are on the line through \((0,5)\) and \((2,8)\).
A:
\((4,11)\)
B:
\((5,10)\)
C:
\((6,14)\)
D:
\((30,50)\)
E:
\((40,60)\)
Problem 2
All three points displayed are on the line. Find an equation relating \(x\) and \(y\).
![Coordinate plane, first quadrant. Line is drawn through 3 comma 3, x comma y, and 6 comma 9](https://cms-im.s3.amazonaws.com/DMg9XQDzFhyTsDv96CYqYFwL?response-content-disposition=inline%3B%20filename%3D%228-8.2.C.PP.Image.07.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.C.PP.Image.07.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T025349Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=366407c9f8830e359121a84ec4825458e4037b48376e512390ae16166b6a1504)
Problem 3
Here is triangle \(ABC\).
![Triangle on graph. A at 2 comma 0, B at 5 comma 0, C at 5 comma 1.](https://cms-im.s3.amazonaws.com/kWE9CbmscGYiHpfH7VEWeV1G?response-content-disposition=inline%3B%20filename%3D%228-8.2.C12.newPP.Image.01.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.C12.newPP.Image.01.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T025349Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=5cf16b3526d682ec33546ae3903ddc89ae08eeda953e43ed26977abe7b0a711a)
- Draw the dilation of triangle \(ABC\) with center \((2,0)\) and scale factor 2.
- Draw the dilation of triangle \(ABC\) with center \((2,0)\) and scale factor 3.
- Draw the dilation of triangle \(ABC\) with center \((2,0)\) and scale factor \(\frac 1 2\).
- What are the coordinates of the image of point \(C\) when triangle \(ABC\) is dilated with center \((2,0)\) and scale factor \(s\)?
- Write an equation for the line containing all possible images of point \(C\).
Problem 4
Here are some line segments.
![Point A, segment B C and 3 other segments, E D, G J and F H.](https://cms-im.s3.amazonaws.com/zdMfaMmDpto438hxcaUeKFDV?response-content-disposition=inline%3B%20filename%3D%228-8.2.A.PP.Image.16.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.A.PP.Image.16.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T025349Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=9d4f1561ff4894fc7210116e1766ed6aea0dcff415cdb827a9a410e54c52e950)
- Which segment is a dilation of \(\overline{BC}\) using \(A\) as the center of dilation and a scale factor of \(\frac23\)?
- Which segment is a dilation of \(\overline{BC}\) using \(A\) as the center of dilation and a scale factor of \(\frac32\)?
- Which segment is not a dilation of \(\overline{BC}\), and how do you know?