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Question 1 of 2
Determine whether the points (2,5)(2,5) and (6,17)(6,17) lie on the line y=3x-1y=3x−1.
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A point satisfies a line if it makes the equation true.
Substitute the given points on the equation to see whether they lie on the line.
Point 1:
((x1x1,,y1y1)) |
== |
((22,,55)) |
|
yy |
== |
33xx-1−1 |
Equation of the line |
55 |
== |
33(2)(2)-1−1 |
Plug in the values |
55 |
== |
6-16−1 |
Simplify |
55 |
== |
55 |
The equation is true |
Point 2:
((x2x2,,y2y2)) |
== |
U(U(6,17) |
|
y |
= |
3x-1 |
Equation of the line |
17 |
= |
3(6)-1 |
Plug in the values |
17 |
= |
18-1 |
Simplify |
17 |
= |
17 |
The equation is true |
Since both equations are true, both points lie on the line y=3x-1
(2,5) and (6,17) lie on the line
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Question 2 of 2
Determine whether the points (3,4) and (2,1) lie on the line y=-x+3.
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A point satisfies a line if it makes the equation true.
Substitute the given points on the equation to see whether they lie on the line.
Point 1:
(x1,y1) |
= |
(3,4) |
|
y |
= |
-x+3 |
Equation of the line |
4 |
= |
-(3)+3 |
Plug in the values |
4 |
= |
-3+3 |
Simplify |
4 |
≠ |
0 |
The equation is false |
Therefore the point (3,4) does not lie on the line y=-x+3
Point 2:
(x2,y2) |
= |
U(2,1) |
|
y |
= |
-x+3 |
Equation of the line |
1 |
= |
-(2)+3 |
Plug in the values |
1 |
= |
-2+3 |
Simplify |
1 |
= |
1 |
The equation is true |
Only the point (2,1) lies on the line y=-x+3