Question

What is the slope-intercept equation of the line that goes through the points 1, 5 and 2, 8​

Answer 1

The slope-intercept equation of the line that goes through the points (1, 5) and (2, 8) is​
`\mathbf{y=(3)/(2)x+(7)/(2) }`

Explanation:

We need to find the slope-intercept equation of the line that goes through the points (1, 5) and (2, 8)

The general equation for slope intercept form is ​
`y=mx+b` where m is slope and b is 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=5, x_2=2, y_2=8`

Putting values and finding slope

`Slope=(y_2-y_1)/(x_2-x_1)\\Slope=(8-5)/(2-1)\\Slope=(3)/(2)`

So, we get slope
`m=(3)/(2)`

Finding y-intercept

y-intercept can be found using slope
`m=(3)/(2)` and point (1,5)

`y=mx+b\\5=(3)/(2)(1)+b\\b=5- (3)/(2)\\b=(10-3)/(2)\\b=(7)/(2)\\`

So, we get y-intercept
`b=(7)/(2)`

Equation of line

So, equation of line having slope
`m=(3)/(2)` and y-intercept
`b=(7)/(2)` is:

`y=mx+b\\y=(3)/(2)x+(7)/(2)`

The slope-intercept equation of the line that goes through the points (1, 5) and (2, 8) is​
`\mathbf{y=(3)/(2)x+(7)/(2) }`