Question

Determine the equation of the line that goes through points (1.1) and (3.7).

Answer 1

The equation of the line that goes through points (1,1) and (3,7) is
`\mathbf{y=3x-2}`

Explanation:

Determine the equation of the line that goes through points (1,1) and (3,7)

We can write the equation of line in slope-intercept form
`y=mx+b` where m is slope and b is y-intercept.

We need to find slope and y-intercept.

Finding Slope

Slope can be found using formula:
`Slope=(y_2-y_1)/(x_2-x_1)`

We have
`x_1=1, y_1=1, x_2=3, y_2=7`

Putting values and finding slope

`Slope=(y_2-y_1)/(x_2-x_1)\\Slope=(7-1)/(3-1)\\Slope=(6)/(2)\\Slope=3`

We get Slope = 3

Finding y-intercept

y-intercept can be found using point (1,1) and slope m = 3

`y=mx+b\\1=3(1)+b\\1=3+b\\b=1-3\\b=-2`

We get y-intercept b = -2

So, equation of line having slope m=3 and y-intercept b = -2 is:

`y=mx+b\\y=3x-2`

The equation of the line that goes through points (1,1) and (3,7) is
`\mathbf{y=3x-2}`