What is the slope of the following line? 4x+2y=12 *

4
8
-2
-4

Slope = -4.000/2.000 = -2.000

x-intercept = 285/2 = 142.50000

y-intercept = 285/1 = 285.00000

Step-by-step explanation: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

4*x+2*y-(12*48-2-4)=0

STEP

1

:

Pulling out like terms

1.1 Pull out like factors :

4x + 2y - 570 = 2 • (2x + y - 285)

Equation at the end of step

1

:

STEP

2

:

Equations which are never true:

2.1 Solve : 2 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Equation of a Straight Line

2.2 Solve 2x+y-285 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 2x+y-285 = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 285/1 so this line "cuts" the y axis at y=285.00000

y-intercept = 285/1 = 285.00000

Calculate the X-Intercept :

When y = 0 the value of x is 285/2 Our line therefore "cuts" the x axis at x=142.50000

x-intercept = 285/2 = 142.50000

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 285.000 and for x=2.000, the value of y is 281.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 281.000 - 285.000 = -4.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = -4.000/2.000 = -2.000

Geometric figure: Straight Line

Slope = -4.000/2.000 = -2.000

x-intercept = 285/2 = 142.50000

y-intercept = 285/1 = 285.00000

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step-by-step explanation:

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