Question

What is the equation of the line that goes through A(3,2) and B(4,1)?

a) What is the slope?
b) What is the y intercept?
c) Use a and b to write the equation
Your answer should be written in the form
a) m =
b) b =
c) y = mx + b

Answer 1

a) m = -1

b) y-intersect = 5

c) y = -x + 5

Step-by-step explanation:

slope (m) = (1-2)/(4-3) = -1/1 = -1

b = 2 - (-1)(3) = 2 + 3 = 5

y = -x + 5

Answer 2

The slope (m) of the line through points A(3,2) and B(4,1) is -1, and the y-intercept (b) is 5. Thus, the equation of the line in slope-intercept form is y = -1x + 5.

Step-by-step explanation:

To find the equation of the line that goes through points A(3,2) and B(4,1), we need to determine the slope and the y-intercept.

a) What is the slope?

The slope (m) is defined as the change in the vertical axis (rise) divided by the change in the horizontal axis (run). In this case:

m = (y2 - y1) / (x2 - x1) = (1 - 2) / (4 - 3) = -1

So, the slope is:
m = -1

b) What is the y-intercept?

Now, we plug one point's coordinates and the slope into the equation y = mx + b to solve for b, the y-intercept.

Using point A(3,2):
2 = (-1)(3) + b
b = 2 + 3

Thus, the y-intercept is:
b = 5

c) Use a and b to write the equation

With m and b known, the equation of the line is:

y = -1x + 5