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.
Since we know the intersecting points for each line, we can use the point-slope form of a linear equation to write the equation for each line.
For Line A:
Using the point-slope form, the equation can be written as:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope of the line.
The two given points on Line A are (0, 7) and (2, 1).
So, we can choose one of these points and the slope between them to write the equation.
Let's use the point (2, 1).
The slope between the two points is: (1 - 7) / (2 - 0) = -6/2 = -3.
Using the point (2, 1) and the slope -3, the equation of Line A can be written as:
y - 1 = -3(x - 2)
Expanding this equation:
y - 1 = -3x + 6
Bringing the y term to the left side:
y + 3x = 5
So, the equation of Line A is y + 3x = 5.
For Line B:
Similar to Line A, we can use the point-slope form to write the equation of Line B.
Using the given points (0, 0) and (3, 7), let's choose the point (3, 7) this time.
The slope between the two points is: (7 - 0) / (3 - 0) = 7/3.
Using the point (3, 7) and the slope 7/3, the equation of Line B can be written as:
y - 7 = (7/3)(x - 3)
Expanding this equation and rearranging:
3y - 21 = 7x - 21
Bringing the y term to the left side:
3y - 7x = 0
So, the equation of Line B is 3y - 7x = 0.
The correct equations for Line A and Line B are:
Line A: y + 3x = 5
Line B: 3y - 7x = 0