Question

Line slope form (3,2),(0,3)

Answer 1

To find the slope of the line passing through the points (3,2) and (0,3), we can use the formula:

m = (y2 - y1) / (x2 - x1)

Where (x1, y1) = (3,2) and (x2, y2) = (0,3).

Plugging in the values, we get:

m = (3 - 2) / (0 - 3)

m = 1 / (-3)

m = -1/3

Therefore, the slope of the line is -1/3.

Now, to write the equation of the line in slope-intercept form (y = mx + b), we need to find the y-intercept (b). We can choose either of the given points to plug into the equation.

Using point (3,2):

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

2 = -1 + b

b = 2 + 1

b = 3

Therefore, the equation of the line passing through the points (3,2) and (0,3) is y = (-1/3)x + 3 in slope-intercept form.