find the equation of straight lines

Question

find the equation of this straight line, m=3, passing through (1,4)

Answer 1

Recall the slope=intercept form of a linear equation:     y = mx + b ,   where m is the slope of the line and b is the y-intercept (point at which line crosses y-axis: (0, b) )

Given:     slope = m = 3    

              (x, y) = (1, 4)   ==>   x = 1 ,   y = 4

     y = mx + b

     4 = 3(1) + b

     4 = 3 + b

     4 - 3 = 3 - 3 + b

     1 = b

Therefore, given that the slope= m= 3 and the y-intercept= b= 1, the equation of the line is as follows:

          y = 3x + 1

Answer 2

 Cwaz,

To solve this linear equation, we want to state it in the slope-intercept form which is y=mx+b

m= slope,   b=y intercept

Since we already know the slope and we have  a pair of coordinates, you can utilize the point-slope form of the equation to solve it.

The point slope form is:  y-y1= m(x-x1)       m=3,  (x1=1, y1=4)

 Therfore   Y-4= 3(x-3)

Use the distributive property to simplify the right side,

Y-4= 3x-3

Add 4 to both sides to isolate y

Y-4+4= 3x-3+4

The final result is  Y= 3X+1.  (This is the equation in slope intercept form.)

 

Answer 3

We know that the equation should be written in the form y=mx + b, where m is the slope and b is the y intercept.  Start by graphing the x and y axis, as well as the point (1.4).  Since m is 3. we know that that is the slope, and that it is positive.  Three is the value of the rise/run.  Since our rise/run must be positive we can use that information to graph a few more points:  go up 3 and to the right 1, (both positive values) OR go down 3 and to the LEFT one (both negative values).  We get the "B" value where x =0: i.e., where our line crosses the y axis, which it does at (0,1)  Since the "y" in this ordered pair is equal to one, we now have our equation: y=3x + 1.

Lauren B.

Answer 4

Start with the equation (y-4)= 3(x-1). Use the distributive property to multiply the 3 by (x-1), yielding this: (y-4)=3x-3. Then get y by itself by adding 4 to both sides, getting this: y=3x+1.  There you have the equation in slope intercept form. If your teacher wants it in standard form (Ax +By=C), then just work from there, by subtracting the 3x from both sides, yielding -3x+y=1.  Hope this helps.