+472 Write an equation in point-slope form for the line through the given point with the given
slope.
1. (10, –9); m = −2
2. (9, –8); m = 5/6
3. (10, 6); m = -2/3
4. (7, 10); m = - 1/2
5. (–1, 2); m = 1
6. A line passes through (2, –1) and (8, 4). Write an equation for the line in point-slope form.
7. A line passes through (4, 3) and (10, 10). Write an equation for the line in point-slope form.
8. A line passes through (–5, –9) and (2, –6). Write an equation for the line in point-slope form.
9. A line passes through (–1, 3) and (10, 9). Write an equation for the line in point-slope form.
10. A line passes through (–7, –3) and (4, 4). Write an equation for the line in point-slope form.
Is the relationship shown by the data linear? If so, model the data with an equation.
11.
| X | Y |
| –9 | -2 |
| -5 | -7 |
| -1 | -12 |
| 3 | -17 |
12.
| X | Y |
| 9 | 1 |
| 15 | 3 |
| 21 | 5 |
| 27 | 7 |
13.
| X | Y |
| -9 | -3 |
| -3 | -2 |
| 3 | 0 |
| 9 | 1 |
14.
| X | Y |
| 5 | -2 |
| 11 | -1 |
| 17 | 0 |
| 23 | 1 |
15.
| X | Y |
| -5 | 1 |
| -1 | 0 |
| 3 | -1 |
| 7 | -2 |
+128474 6. A line passes through (2, –1) and (8, 4). Write an equation for the line in point-slope form.
( x1, y1) (x2 , y2)
Use the above to find the slope, m, which is given by :
m = [ y2 - y1] / [ x2 - x1] = [4 - (-1)] / [ 8 - 2) = 5/6
Then..... just use one of the points (either one, doesn't matter) and do what we just did in 1 -5
y - 4 = (5/6)(x - 8)
This example should get you through number 10
I'll finish the rest in a little while
+128474 Sorry, Haley.....they wanted point-slope form....here we go
These examples should cover every problem 3 - 5.......
Point-slope form .......y - y1 = m(x - x1)
1. (10, –9); m = −2 → y - (-9)= -2(x - 10)
2. (9, –8); m = 5/6 → y - (-8) = (5/6) (x - 9)
+128474 6. A line passes through (2, –1) and (8, 4). Write an equation for the line in point-slope form.
( x1, y1) (x2 , y2)
Use the above to find the slope, m, which is given by :
m = [ y2 - y1] / [ x2 - x1] = [4 - (-1)] / [ 8 - 2) = 5/6
Then..... just use one of the points (either one, doesn't matter) and do what we just did in 1 -5
y - 4 = (5/6)(x - 8)
This example should get you through number 10
I'll finish the rest in a little while
+128474 11.
X Y
–9 -2
-5 -7
-1 -12
3 -17
OK Haley ....this isn't difficult....just time consuming
If the differences in the x's and y's are constant, we have a line....if not, we don't
Notice that the difference in one x to another reading downward is +4
For example -9 + 4 = -5 and -5 + 4 = -1 and -1 + 4 = 3 ...... etc.
And the difference in one y to another reading downward is also constant = -5
For example -2 - 5 = -7 and -7 - 5 = -12 ........etc
So...if we have a line......as we did in number 6.....use any two of the points to find the slope and then write the equation
For exampe in 11, we can use ( -9, -2) and (-5, -7)
( x1, y1 ) (x2, y2)
The slope = m = [y2 - y1] / [ x2 - x1] = [-7 - (-2)] / [-5 - (-9)] = -5 / 4
And the equation .....in point-slope form is
y - (-7) = (-5/4) [ x - (-5)] [remember that we can use any point on the line in this equation]
The rest are similar.........if the differences in x's and y's are not constant......we don't have a line so don't worry about writing an equation in that case
[13 is not a line...the y's are not constant......don't worry about it....!!! ]
