3x+5y_10=0 and y=_3over 5x-3
On one cartesian plane graph both of following equations using the slope and y intercept method
To use the slope-intercept method, we need to rearrange the first equation into the form y=mx+b, where m is the slope and b is the y-intercept:
3x + 5y = -10
5y = -3x - 10
y = (-3/5)x - 2
For the second equation, we already have it in the form y=mx+b, but we need to simplify the fraction:
y = (-3/5)x + 3/5
Now we can graph both equations on the same Cartesian plane. To do this, we'll plot a few points for each equation and then draw a line through them.
For the first equation, we can start with the y-intercept of -2:
y = (-3/5)x - 2
y = (-3/5)(0) - 2
y = -2
So one point on the line is (0,-2).
For another point, we can use the slope of -3/5 to move down 3 units and to the right 5 units:
y = (-3/5)x - 2
y = (-3/5)(5) - 2 + 3
y = -5 + 1
y = -4
So another point on the line is (5,-4).
We could find more points if needed, but these two are enough to draw the line:
(0,-2) --------- (5,-4)
Next, we'll graph the second equation:
y = (-3/5)x + 3/5
For this equation, we can start with the y-intercept of 3/5:
y = (-3/5)x + 3/5
y = (-3/5)(0) + 3/5
y = 3/5
So one point on the line is (0,3/5).
For another point, we can use the slope of -3/5 to move down 3 units and to the right 5 units:
y = (-3/5)x + 3/5
y = (-3/5)(5) + 3/5 - 3
y = -3
So another point on the line is (5,-3).
Again, these two points are enough to draw the line:
(0,3/5) --------- (5,-3)
Now both lines are graphed on the same Cartesian plane:
|
4 |
| /
3 | /
| /
2 |
|
1 | /
| /
0 | / (0,3/5)
|
------|------|------|------|------
-5 -4 -3 -2 -1 0 1 2 3 4 5
| | | | |
(0,-2) (5,-4)