How do you find the y intercept given (44.2, -22.8) and (25.2, 34.2)?

1 Answer
Nov 3, 2015

Answer:

Calculate the slope, hence the equation of the line in point slope form, hence the equation of the line in slope intercept form, hence the intercept #(0, 109.8)#

Explanation:

Given two points:

#(x_1, y_1) = (44.2, -22.8)#

#(x_2, y_2) = (25.2, 34.2)#

The slope #m# of the line through these points is given by the formula:

#m = (Delta y)/(Delta x) = (y_2-y_1)/(x_2-x_1) = (34.2-(-22.8))/(25.2-44.2) = 57.0/-19.0 = -3#

Then we can express the equation of the line in point slope form as:

#y - y_1 = m(x - x_1)#

That is:

#y - (-22.8) = -3(x-44.2)#

That is:

#y + 22.8 = -3x+132.6#

Subtract #22.8# from both sides to get:

#y = -3x+109.8#

This is in slope intercept form, the intercept being #109.8#

So the line intercepts the #y# axis at #(0, 109.8)#