Question

The equation of the line passing through the points (4, 15) and (2, 25) can be expressed as y = mx + b. Give the value of b.

Answer 1

Slope formula: y1-y2/x1-x2=m, given that x and y are coordinates and m is the slope. You have two sets of coordinates in your question, so I will first use those to find the slope of the equation:

15-25/4-2=m

This reduces to -10/2, or -5.

Slope intercept form: y=mx+b, given m is the slope and b is the y-intercept. Plug the slope in now.

y=-5x+b

Now, use one of the coordinates in the question to solve for b. I'm using (4,15).

15=-5(4)+b

15=-20+b

Add 20 to both sides.

35=b

Your equation is: y=-5x+35

and b=35

I hope this helps :)

Answer 2

Equation of any line is given by y-mx+b where m is the slope and b is the y intercept.

Two points are given to us .Let us first find the slope

Slope of the points (4,15) and (2,25) is the difference of y divided by difference of x coordinate

m=
`(25-15)/(2-4)=(10)/(-2) =-5`

Slope m= -5 and any (x,y)=(4,15)

We put these values in y=mx+b to find b (Any of the two given points can be taken as (x,y)

15=-5(4)+b

15=-20+b

Adding 20 both sides

15+20=-20+20+b

35=b

Or b=35.