Question

Write an equation in slope-intercept form of the line that passes through $(6,\ 11)$ and $(2,\ \frac{25}{3})$

Answer 1

The equation of the line is y=− 4/3 x+13.

To find the equation of the line passing through the points (6,11) and (2, 25/3), we can use the slope-intercept form of a linear equation, which is given by:

y=mx+b

The slope (m) can be calculated using the formula:

m=
`y_2-y_1/x_2-x_1`

Let (x1 ,y​1 )=(6,11) and (x​2 ,y2​)=(2, 25/3 ).

Putting values we get,

m= -1/3

Now that we have the slope, we can use one of the points (let's use (6,11)) to substitute into the equation to solve for b:

11=− 1/3(6)+b

11=−2+b

b=13

Therefore, the equation of the line is y=− 1/3x+13. To put it in slope-intercept form, we can multiply both sides by 3 to clear the fraction:

3y=−x+39

y=− 1/3x+13

So, the equation of the line passing through the given points is y=− 1/3x+13.