Question

What is the equation of the line in slope-intercept form that passes through the points (0, 3) and (4, 2)?

a) y = -0.25x + 3
b) y = -0.25x + 2
c) y = 0.25x + 3
d) y = 0.25x + 2

Answer 1

The equation of the line in slope-intercept form that passes through the points (0, 3) and (4, 2) is y = -0.25x + 3.

Step-by-step explanation:

To find the equation of the line in slope-intercept form, we first need to find the slope of the line. The slope is the change in y divided by the change in x between the two points. So, using the points (0, 3) and (4, 2), we can calculate the slope as follows:

1. Change in y = 2 - 3 = -1
2. Change in x = 4 - 0 = 4
3. Slope = (-1)/(4) = -0.25

Now that we have the slope, we can use the point-slope form of the equation of a line to find the y-intercept. The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Using the point (0, 3):

1. x1 = 0, y1 = 3, m = -0.25
2. y - 3 = -0.25(x - 0)
3. y - 3 = -0.25x
4. y = -0.25x + 3

Therefore, the equation of the line in slope-intercept form that passes through the points (0, 3) and (4, 2) is y = -0.25x + 3.