Math help? linear equations in two variables.?

Question

Find the equation of the line which passes thru (2,4) and (3,5)

Pls show step by step solution. Thank you mate

Thank you for all that helpd

Answer 1

Thru (2, 4) and (3, 5)

Your first step is to determine the slope. Recall that the slope formula is

m = (y2 - y1)/(x2 - x1)

In this case, (x1, y1) = (2, 4) and (x2, y2) = (3, 5).

m = (5 - 4)/(3 - 2)
m = 1/1
m = 1

Now that we have slope m = 1, we use the slope formula once more to find the equation of the line. This time, we use
(x1, y1) = (2, 4) and (x2, y2) = (x, y), with m = 1.

(y2 - y1)/(x2 - x1) = m
(y - 4)/(x - 2) = 1
y - 4 = 1(x - 2)
y = x - 2 + 4
y = x + 2

Answer 2

Points(2,4) and (3,5)

Standard form of linear equation is

y = mx + b
m = slope
b = y-intercept (value of x when y = 0)

Slope = m = 5-4/3-2 = 1/1 = 1
m = 1
Substitution
y = 1(x) + b
y = x + b
__________
Take point (2,4)
Substitute these values to the eqaution to find b
4 = 2 + b
4-2 = 2 - 2 + b
2 = b
Let's try Point (3,5) if we can get the same value of b
5 = 3 + b
5-3 = 3-3 + b
2 = b
________________________
From our calculation, we
find m = 1
and b = 2
Therefore our equation is
y = x + 2 ===> the answer.

To learn more about slopes, visit this site ===>
http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut15_slope.htm

Answer 3

Using the point-slope method,
slope, m = (5 - 4)/(3 - 2) = 1
(y - 4)/(x - 2) = 1
y - 4 = x - 2
y = x + 2

or

y = mx + b
4 = 2m + b
5 = 3m + b
m = 1
4 = 2*1 + b
b = 2
y = x + 2

Answer 4

use the line formula y= mx +c.
so with the given information:

4 = 2m + c ----- (1)
5 = 3m + c ----- (2)

so from (1):
c= 4 - 2m
sub into (2) gives:
5= 3m + (4 -2m)
hence 5-4 = (3-2)m
therefore m=1,

sub into (1) [or 2 your choice]
gives c = 2

and the line equation is y = x + 2

Answer 5

2 basic basic procedures to unravel: #a million: removing x+2y=0 2x-6y=5 Multiply equation a million via 3 3x+6y=0 2x-6y=5 -----------upload 5x=5 x=a million replace a million for x into the two of the two unique equations. x+2y=0 a million+2y=0 2y=-a million y= -a million/2 #2: Substitution x+2y=0 2x-6y=5 From Equation No.a million, x=-2y replace x with -2y in Equation No.2 2(-2y)-6y=5 -4y-6y=5 -10y=5 y= -a million/2 As until now, replace y with -a million/2 in the two unique equation. 2x-6y=5 2x-6(-a million/2)=5 2x+3=5 2x=2 x=a million Take your %.!

Answer 6

m = (5 - 4) / (3 - 2)
m = 1
y - 4 = 1.(x - 2)
y - 4 = x - 2
y = x + 2