Question

Write the equation of the line passing through the points (-1,2) and (3,4)

Answer 1

`{y=(1)/(2)x+(5)/(2)`

Explanation:

We can write the equation in slope intercept form.

`y=mx+b`

Finding Slope:

Slope is (rise/run).
`m=(y_2-y_1)/(x_2-x_1)`

We are given the points (-1,2) and (3,4).

`(4-2)/(3+1)=(2)/(4)=(1)/(2)`

The slope is 1/2.

Finding Y-intercept:

We can use the equation
`y=(1)/(2)x+b` to solve for the y-intercept.

Replace 'y' and 'x' with a given point and solve for 'b'. I will use (3,4).

`4=(1)/(2)(3)+b\\\\4=(3)/(2)+b\\\\(3)/(2)+b=4\\\\(3)/(2)-(3)/(2)+b= 4-(3)/(2)\\\\`

`b=(5)/(2)`

The y-intercept is 5/2.

Final Equation:

As stated above, slope intercept form is
`y=mx+b`. 'M' is the slope and 'b' is the y-intercept.

We are given the slope of 1/2 and the y-intercept of 5/2.

`y=mx+b\rightarrow\huge\boxed{y=(1)/(2)x+(5)/(2)}`