Question

What equation in slope-intercept form represents the line that passes through

the points (1,3) and (2,5)?

Answer 1

So, equation in slope-intercept form that represents the line that passes through the points (1,3) and (2,5) is y=2x+1

Explanation:

We need to write equation in slope intercept form that represents the line that passes through the points (1,3) and (2,5)

The standard equation of slope-intercept form is: y= mx+b

where m is the slope of the lines and b is the y-intercept.

To make the equation we need to find slope (m) and y-intercept (b)

Find Slope

The formula to find slope m is:
`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

We have
`x_(1)=1, x_(2)=2, y_(1)=3\ and \ y_(2)=5`

Putting values in the formula to find slope

`m=(y_(2)-y_(1))/(x_(2)-x_(1))\\m=(5-3)/(2-1)\\m=(2)/(1)\\m=2`

So, value of slope m is m=2

Find y-intercept

Using formula of slope-intercept formula we can find b

y=mx+b

Using point (1,3) (where x=1 ,y=3) and slope m=2

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

So, value of y-intercept b is: b=1

Required equation in Slope Intercept Form

We have slope m = 2 and y-intercept b=1

`y=mx+b\\y=2x+1`

So, equation in slope-intercept form that represents the line that passes through the points (1,3) and (2,5) is y=2x+1