I need to know how to write an equation in standard form of the line that passes through the two points.?

Question

The question is (1,4), (5,7). And I know you start out Y=mx+b

and so far I got y=3/4x+b.
But this is where I get stuck. How do you find out what B is from the two points givin?
The teacher wont explain it to me and I was absent the day she went over it.

Answer 1

find b by putting either x value (1 or 5) in for x in the equation, and then the corresponding y value (4 or 7) in for y in the equation, and then solve.

4=(3/4)*1 + b
b=16/3

y=(3/4)x + 16/3

Standard form means 0= blah blah & the first coefficient is positive.

12 y= 9x + 64
0 = 9x-12y + 64

Answer 2

del x = (x1 - x2) = x at point 1 minus x at point 2
del y = (y1 - y2) = y at point 1 minus y at point 2

point 2 = (1,4); point 1 = (5,7)

slope = m = del y/del x = (y1 - y2)/(x1 - x2) = 3/4

The general equation for a straight line in Cartesian coordinates is y = mx + b; so that y = (3/4)x + b and we need to find b.

To find the intercept (b), set point 2 = (0,y) and leave point 1 as is. Thus, m = (7 - y)/(5 - 0) = 3/4 = (7 - y) = 15/4; so that, y = 7 - 15/4 = 13/4 = b because, from y = mx + b we see that y = b when x = 0. In other words, point 2 (x2,y2) becomes (0,b).

Thus your general equation is y = (3/4)x + 13/4 or 4y = 3x + 13.

Lesson learned: Find the slope first via m = del y/del x; then use the found m and redo m = del y/del x with x2 = 0 and y2 = b to find the intercept b.

Answer 3

I method: The equation of a straight line passing through the two points (a,b) and (c,d) is :
y - b = ((d-b)/(c-a))( x-a).
For the points (1,4) and (5,7) . we get:
y-4 = (3/4) (x - 1) or 4y - 16 = 3x - 3 Or
3x - 4y +13 =0. Answer.
Verify : OK
II method: Following you, let the equation of the straight be
y=mx +c
It passes through (1,4), so 4 = m +c..........(1)
It passes through (5,7), so 7 = 5m +c.........(2)
Solving (1) and (2), we get :
m = 3/4 ( as you did) and c= 13/4.
So the Eq. is y = (3/4) x +(13/4)
which leads to 3x - 4y +13 = 0, as before.

Answer 4

All you have to do is plug in the x and y value from either ordered pair. Then solve for b.

Given: (1,4) and (5,7)
y=3/4x+b

we will use x=1 and y=4
4=3/4(1)+b
4=3/4+b
13/4=b

Now, we'll use x=5 and y=7
7=3/4(5)+b
7=15/4+b
13/4=b

Now we definetely know that b=13/4.

Answer 5

Slope intercept form

y = mx + b

Ordered pair

(1, 4)

4 = 3/4(1) + b

4 / 1 x 4 / 3 = 4 / 3(3 / 40 + b

16 / 3 = b

- - - - - - - - --

Slope intercept form

y = mx + b

Ordered pair

(5, 7)

7 = 3/4(5) + b

7 = 15/4 + b

7/1 x 4 / 15 = 4 / 15(4 / 15) + b

28 / 15 = b

- - - - - - - - -s-

Answer 6

x1 = - 2 y1 = one million x2 = 2 y2 = 4 m = (y2 - y1) / (x2 - x1) m = (4 - one million) / [2 - (- 2)] m = 3 / (2 + 2) m = 3/4 b = y - mx .......... (Use the two y-coordinate) b = 4 - 3/4(2) b = 4 - 6/4 b = sixteen/4 - 6/4 b = 10/4 b = 5/2 Equation of Line: y = 3/4 x + 5/2 or 3/4 x - y = - 5/2 or 4(3/4 x) - 4(y) = 4(- 5/2) 3x - 4y = - 10 ¯¯¯¯¯¯¯¯¯¯¯¯  

Answer 7

m=3/4

Use point-slope

y-4=(3/4)(x-1)
y-4=(3/4) x - 3/4
4y-16=3x-3
-16=3x-4y-3
-13=3x-4y