Question

What is the y - intercept of the line that goes through the points (4,3) and (8,2) ?

Answer 1

First, we need to find the slope of the line:

slope = (change in y) / (change in x)

slope = (2 - 3) / (8 - 4)

slope = -1/4

Now we can use the point-slope formula to find the equation of the line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is one of the given points. Let's use (4,3):

y - 3 = (-1/4)(x - 4)

Simplifying:

y = (-1/4)x + 4 + 3

y = (-1/4)x + 7

The y-intercept occurs when x = 0, so we can substitute that into the equation to find the y-intercept:

y = (-1/4)(0) + 7

y = 7

Therefore, the y-intercept of the line that goes through the points (4,3) and (8,2) is 7.