Question

Write an equation in slope-intercept form of the line passing through (0,3) and (2, -1).A.y= -2x + 3B.y= 2x + 3C.y= -x +3D. y = -2x

Answer 1

We are asked to find the equation in slope-intercept form that passes through the following points.

`(0,3)\text{ and }(2,-1)`

Recall that the equation of the line in slope-intercept form is given by

`y=mx+b`

Where m is the slope and b is the y-intercept.

The slope of the line is given by

`m=(y_2−y_1)/( x_2−x_1)`
`\text{where}(x_1,y_1)=(0,3)\text{and}(x_2,y_2)=(2,-1)`

Let us substitute the given values into the above slope formula

`m=(-1-3)/(2-0)=-(4)/(2)=-2`

So the equation of line becomes

`y=-2x+b`

Now let us find the y-intercept (b)

Choose any one point from the given two points

Let choose (0, 3) and substitute it into the above equation.

`\begin{gathered} y=-2x+b \\ 3=-2(0)+b \\ 3=0+b \\ 3=b \\ b=3 \end{gathered}`

Please note that even if you had chosen any other point then still you would have gotten the same y-intercept.

Therefore, the equation of the line in slope-intercept form is

`y=-2x+3`

The correct option is A.