Question

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).

Answer 1

To find the equation of each line, we can use the slope-intercept form, which is given by:

y = mx + b

where m is the slope of the line and b is the y-intercept.

For Line A:
We can find the slope (m) using the formula:
m = (y2 - y1)/(x2 - x1)

Substituting the given points (0, 7) and (2, 1) into the formula, we have:
m = (1 - 7)/(2 - 0)
m = -6/2
m = -3

Now that we have the slope, we can substitute it along with one of the points into the slope-intercept form to find the y-intercept (b). Let's use the point (2, 1):

1 = -3(2) + b
1 = -6 + b
b = 1 + 6
b = 7

So the equation of Line A is:
y = -3x + 7

For Line B:
Similarly, we can find the slope (m) using the formula:
m = (y2 - y1)/(x2 - x1)

Substituting the given points (0, 0) and (3, 7) into the formula, we have:
m = (7 - 0)/(3 - 0)
m = 7/3

Now we can substitute the slope and one of the points into the slope-intercept form to find the y-intercept (b). Let's use the point (3, 7):

7 = (7/3)(3) + b
7 = 7 + b
b = 7 - 7
b = 0

So the equation of Line B is:
y = (7/3)x + 0
y = (7/3)x

In summary, the equations of the two lines are:
Line A: y = -3x + 7
Line B: y = (7/3)x