Question

What is the y intercept? how to use the point-slope formula to solve?

Answer 1

Given:

The coordinates of points is

(x1, y1)=(4, 2)

(x2, y2)=(2, -5).

The slope of the line passing through points (x1, y1)=(4, 2) and (x2, y2)=(2, -5) is,

`\begin{gathered} m=(y2-y1)/(x2-x1) \\ m=(-5-2)/(2-4) \\ m=(-7)/(-2) \\ m=(7)/(2) \end{gathered}`

The point slope form of the equation of a line can be written as,

`y-y1=m(x-x1)`

Put (x1, y1)=(4, 2) in the above equation to find the equation of a line with slope m=7/2 and passing through (4,2).

`\begin{gathered} y-2=(7)/(2)(x-4) \\ 2(y-2)=7(x-4) \\ 2y-2*2=7x-4*7 \\ 2y-4=7x-28 \\ 2y=7x-28+4 \\ 2y=7x-24 \\ y=(7)/(2)x-(24)/(2) \\ y=(7)/(2)x-12\text{ ----(1)} \end{gathered}`

The general equation of a straight line is,

`y=mx+b\text{ ------(2)}`

Here, m is the slope of the line and b is the y intercept.

Comaparing equations (1) and (2), we get y intercept b=-12.

Therefore, the y intercept b=-12.

The equation of the line is,

`y=(7)/(2)x-12\text{ -----(3)}`

We have to check if (-4, -2) is a point on the line.

For that put x=-4 in equation (3) and solve for y to check if we get y=-2.

`\begin{gathered} y=(7)/(2)*(-4)-12 \\ =-14-12 \\ =-26 \end{gathered}`

Since we got y=-26 instead of , (-4, -2) is not a point on the line.