# Quick problem: given the slope and a point, find the line

#### tmt

##### Active member
Hello,

I am working on a problem. I am trying to get an equation for this linear line with these traits:

slope = 5/6

linear equation that passes through [1,3]

therefore using this formula

y=mx+b

3=5/6+b

b=13/6

therefore, the equation is

y=5/6[x] + 13/6

y - ( 3 ) = (5/6) ( x - ( 1 ) ) ,

or

y = (7/6) x + (13/6) .

Any pointers,

Thanks, Tim

#### MarkFL

Staff member
The second given answer has the wrong slope. I would recommend using the point-slope formula because you are given exactly what you need to use this formula, that is a point on the line and its slope.

This formula is:

$$\displaystyle y-y_1=m\left(x-x_1 \right)$$

Now, you are given:

$$\displaystyle m=\frac{5}{6}$$

and:

$$\displaystyle \left(x_1,y_1 \right)=(1,3)$$

And so plugging in the given data to our formula, we obtain:

$$\displaystyle y-3=\frac{5}{6}(x-1)$$

If we wish to put this into slope-intercept form, we may distribute the slope on the right side:

$$\displaystyle y-3=\frac{5}{6}x-\frac{5}{6}$$

$$\displaystyle 3=\frac{18}{6}$$

to get:

$$\displaystyle y=\frac{5}{6}x+\frac{13}{6}$$

So you had the correct answer in slope-intercept form, but the answer given by your book is incorrect for this form (the slope is wrong, most likely just a typo), but is correct for the point-slope form.

#### Deveno

##### Well-known member
MHB Math Scholar
A persistent problem with many math texts is that "answers" given in the "back of the book" often contain silly mistakes (apparently, good proof-readers are hard to find).

The only remedy for this is to become so confident in YOUR skills, that you can TELL when the answer is right or wrong.

You answered the problem correctly, so well done!