Line passes through the points (-2.6,1) and (1.4​,2.5) as shown. Find the equation of the line that passes through (0,-b) and (c,0) .

Question

I need an equation

Answer 1

My approach: (there are several)

The general form of a linear equation is: y = mx + b where m is the slope and b is the y-intercept.

Find the slope by dividing the change in y by the change in x:

y changes from 1 to 2.5 so we divide +1.5 by the change in x

x changes from -2.6 to 1.4 so we divide 1.5 by 4

m = 3/8

To find b, solve either one of the equations by substituting the values of x and y (I illustrate both):

1 = (3/8) * (-2.6) + b -> 1 = -39/40 + b -> b = 1 39/40

2.5 = (3/8) * (1.4) + b -> 2.5 = 21/40 + b -> b = 1 39/40

One should not be surprised that both equations yield the same value of b ;)

Answer 2

First, use the two point to determine the slope of the line. In this case m = (2.5-1)/(1.4+2.6) = 0.375

Next use the formula y = mx + a by plugging in our found value of m and one of the two point to solve for a.

2.5 = 0.375 * 1.4 + a => a = 3.025

Now we have the full equation of the line is y = 0.375x + 3.025

It is not clear how to go from this. It looks like the question has a graph included. Would you like to share it here?