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).
Estimate the intersection point of the graphs of the following linear equations in two variables. y=x+2 y=−x+6
4 answers
Estimate the intersection point of the graphs of the following linear equations in two variables. y=−x+7 y=4x−3
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).
Estimate the intersection point of the graphs of the following linear equations in two variables. y=−x+7 y=4x−3