The graphs of two lines are shown.
Graph 1 titled 'Line A' has the intersecting points at (0, 7) and (2, 1). Graph 2 titled 'Line B' has the intersecting points at (0, 0) and (3, 7).
Drag the correct equation for each line to the appropriate box.
Line A (Graph 1) equation: y = -3x + 7
Line B (Graph 2) equation: y = 2x
line b is wrong
Apologies for the incorrect response. Let us calculate the equation for Line B accurately.
To find the equation for Line B, we need to calculate the slope and y-intercept using the given points (0, 0) and (3, 7).
Slope (m) = (change in y) / (change in x)
= (7 - 0) / (3 - 0)
= 7/3
Using the slope-intercept form (y = mx + b), we can substitute the slope and any point (x, y) to find the y-intercept (b).
0 = (7/3)(0) + b
0 = b
Therefore, the equation for Line B is: y = (7/3)x.
Unfortunately, as an AI text-based bot, I am unable to see or interpret images or graphics. However, I can help you determine the equation of each line using the given points. To find the equation of a line, we can use the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
For Line A:
Using the points (0, 7) and (2, 1), we can calculate the slope using the formula:
m = (y2 - y1) / (x2 - x1)
= (1 - 7) / (2 - 0)
= -6 / 2
= -3
Now that we have the slope, we can choose any one of the given points and substitute it into the equation y = mx + b to solve for b.
Using (0, 7), we have:
7 = -3(0) + b
7 = b
Therefore, the equation of Line A is: y = -3x + 7
For Line B:
Using the points (0, 0) and (3, 7), we can calculate the slope:
m = (y2 - y1) / (x2 - x1)
= (7 - 0) / (3 - 0)
= 7 / 3
Using (0, 0), we can substitute into the equation y = mx + b:
0 = (7/3)(0) + b
0 = b
Therefore, the equation of Line B is: y = (7/3)x + 0, which simplifies to y = (7/3)x.
Based on this information, you can drag the correct equations to the corresponding boxes.
To find the equation of a line, we can use the slope-intercept form, which is given by:
y = mx + b
where m represents the slope of the line and b represents the y-intercept.
For Line A, we need to find the slope (m) and the y-intercept (b) using the given intersecting points.
Step 1: Find the slope (m):
The slope, m, can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Using the given intersecting points for Line A, (0, 7) and (2, 1), we have:
m = (1 - 7) / (2 - 0)
m = -6 / 2
m = -3
Step 2: Find the y-intercept (b):
We can choose any point on the line (x, y) and substitute it into the equation y = mx + b to find the y-intercept (b).
Using the point (2, 1), we have:
1 = (-3)(2) + b
1 = -6 + b
b = 1 + 6
b = 7
So, the equation for Line A is y = -3x + 7.
Now let's move on to Line B.
Using the same steps as for Line A, we can find the equation for Line B.
Step 1: Calculate the slope (m):
m = (y2 - y1) / (x2 - x1)
Using the given intersecting points for Line B, (0, 0) and (3, 7), we have:
m = (7 - 0) / (3 - 0)
m = 7 / 3
Step 2: Find the y-intercept (b):
Using the point (3, 7), we can substitute it into the equation y = mx + b to find the y-intercept (b).
7 = (7/3)(3) + b
7 = 7 + b
b = 7 - 7
b = 0
So, the equation for Line B is y = (7/3)x + 0, which simplifies to y = (7/3)x.
By using these steps, we have found the equations for Line A and Line B.