Slope is 3, and (1,4) is on the line.

Question

Use the information given to write an equation in standard form

Answer 1

The Standard Form of the equation of a line is:   Ax+By=C.

 

Now, once and forever, convert that to the slope-intercept form of the equation of a line (y=mx+b) and remember that the slope, m, is (-A/B).

 

Given a slope of 3, the equation looks like:    3x - y = C   [note: -3/(-1) = 3]     and we need point (1,4) to find C.

    3(1) - 4 = C

     -1 =  C

 

The equation of the line, in Standard Form, is:    3x - y = -1

   

Answer 2

We can use the point-slope form of the line as a starting point.

 

y - y₁ = m(x - x₁)

 

y - y₁ = mx - mx₁

 

 

Since we need the standard form, which is    Ax+By=C, we manipulate the point-slope form.

 

-mx + y = -mx₁ + y₁      ----> standard form

 

 

where:

m is the slope

(x₁ , y₁) is the given point

 

 

Just plug in the known values into the standard form.

Answer 3

Hi Mallory,

We know that in standard form, a line will have the equation y=mx+b, where m is the slope and b is the y-intercept.
Based on the given information, we know we can immediately replace m in the standard form equation with the given slope, 3

 

y=mx+b

y=3x+b

 

Now, we just have to solve for b, the y-intercept! We can do this by plugging in the (x,y) coordinates given to us and then solving for b:

y=3x+b

4=3(1)+b

4=3+b

1=b

 

So plugging b=1 into our standard form gives us:

y=3x+1

 

Solution: y=3x+1