Asked by Mujika
Estimate the intersection point of the graphs of the following linear equations in two variables. y=x+2 y=−x+6
Answers
Answered by
GPT 3.5
To find the intersection point of two linear equations, we can set the equations equal to each other and solve for x.
So, x + 2 = -x + 6.
Combining like terms, we get 2x + 2 = 6.
Subtracting 2 from both sides, we have 2x = 4.
Dividing both sides by 2, we get x = 2.
To find the y-coordinate of the intersection point, we can substitute the value of x into either of the original equations. Let's use the first equation, y = x + 2.
Substituting x = 2, we get y = 2 + 2 = 4.
Therefore, the intersection point of the two graphs is (2, 4).
So, x + 2 = -x + 6.
Combining like terms, we get 2x + 2 = 6.
Subtracting 2 from both sides, we have 2x = 4.
Dividing both sides by 2, we get x = 2.
To find the y-coordinate of the intersection point, we can substitute the value of x into either of the original equations. Let's use the first equation, y = x + 2.
Substituting x = 2, we get y = 2 + 2 = 4.
Therefore, the intersection point of the two graphs is (2, 4).
Answered by
Mujika
Estimate the intersection point of the graphs of the following linear equations in two variables. y=−x+7 y=4x−3
Answered by
GPT 3.5
To estimate the intersection point of the two linear equations, let's plot the lines on a graph.
The first equation, y = -x + 7, has a y-intercept of 7 and a slope of -1. This means that for every increase of 1 in x, y decreases by 1. We can plot a point at (0, 7) and then use the slope to find another point. From (0, 7), we can move 1 unit to the right and 1 unit down to get (1, 6), and then repeat to get (2, 5).
The second equation, y = 4x - 3, has a y-intercept of -3 and a slope of 4. This means that for every increase of 1 in x, y increases by 4. We can plot a point at (0, -3) and then use the slope to find another point. From (0, -3), we can move 1 unit to the right and 4 units up to get (1, 1), and then repeat to get (2, 5).
Now, let's plot these points and draw the lines:
Graph:
|
7 | x +
| +
| +
| +
2 |+
|
---------------------
0 1 2 3 4
From the graph, we can estimate that the intersection point is approximately (2, 5).
The first equation, y = -x + 7, has a y-intercept of 7 and a slope of -1. This means that for every increase of 1 in x, y decreases by 1. We can plot a point at (0, 7) and then use the slope to find another point. From (0, 7), we can move 1 unit to the right and 1 unit down to get (1, 6), and then repeat to get (2, 5).
The second equation, y = 4x - 3, has a y-intercept of -3 and a slope of 4. This means that for every increase of 1 in x, y increases by 4. We can plot a point at (0, -3) and then use the slope to find another point. From (0, -3), we can move 1 unit to the right and 4 units up to get (1, 1), and then repeat to get (2, 5).
Now, let's plot these points and draw the lines:
Graph:
|
7 | x +
| +
| +
| +
2 |+
|
---------------------
0 1 2 3 4
From the graph, we can estimate that the intersection point is approximately (2, 5).
Answered by
Monicarosefromlosa27
Estimate the intersection point of the graphs of the following linear equations in two variables. y=−x+7 y=4x−3