How do you write an equation of a line????

Question

That passes through these points:
( 2, 4) and ( 4, -5)

Answer 1

x2 - x1 = 4 - 2 = 2

y2 - y1 = -5 - 4 = - 9

So, slope m = - 9 / 2

When x = 0, y = 4 + 9 = 13

So, the equation is

y = - 9x/2 + 13

Check by substituting values of x in that equation.

Answer 2

The general equation of straight line is given by:
Ax + By = C
where A, B and C are constants and A and B cannot be both zero.

Slope intercept form of a Line:
The equation of a line with a defined slope m can also be written as follows:
y = mx + b
where m is the slope of the line and b is the y intercept of the graph of the line.

Slope of a Line:
If a line passes through two distinct points P1(x1 , y1) and P2(x2, y2), its slope is given by:
m = (y2 - y1) / (x2 - x1)
with x2 not equal to x1.

now to answer your math problem we just need substitute your givens:-)

solution:
write an equation of a line which passes through these points:
p1( 2, 4) and p2( 4, -5).

solve for the slope:
m = (y2 - y1) / (x2 - x1)
m = (-5 - 4 ) / (4 - 2) = -9/2

solve for y intercept using p1(2,4) and m=-9/2
y = mx + b
4=(-9/2)(2) + b
4 = -9 + b
b = 4+9 = 13

now having computed the value of m and b substitute them to the line equation of a line which is y = mx + b

your line equation will be:

9x/2 + y = 13 (general equation)
or
y = (-9/2)x + 13 (Slope intercept form of a Line)
or
y = -9x/2 +13

enjoy math:-)

Answer 3

The general equation of a line is y=mx+b, where m is the slope of the line and b is a constant commonly called the y-intercept. The slope of a line is always equal to (y1-y0)/(x1-x0). In this case, the slope would equal [(-5)-4]/(4-2). This reduces to -9/2. Now that we have the slope, we can pick a set of points, substitute them into our equation for x and y, and then solve for b.

y = (-9/2)x + b Lets use (2,4) as our set of points.
4 = (-9/2)(2) + b
b = 13

Now just plug b back into the general equation of the line along with your slope and you have your answer.

y = -9/2x + 13


Note: b is called the y-intercept because when you substitute x=0 into your equation and solve for y, you will always get y = b as your answer. When x ='s 0, your line is passing through the y axis. The point at which is passes or intercepts the y-axis is called the y-intercept.

Answer 4

for linear equation , we have y=mx+b where m is slope and b is y-intercept

slope = (-5-4)/( 4-2)
= -9/2
4= -9/2( 2) + b
b= 13

so, y= -9/2x+13

Answer 5

(y - 4) / (x - 2) = (- 5 - 4) / (4 - 2)
(y - 4) = - (9/2)(x - 2)
y = - (9/2)x + 13
or
9x + 2y = 26