Question

5. Find the slope of the line
4x + 16y = 12

Answer 1

4*x+16*y-(12)=0

4x + 16y - 12 = 4 • (x + 4y - 3)

y=mx+b

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 x+4y-3 = 0 and calculate its properties.

Notice that when x = 0 the value of y is 3/4 so this line "cuts" the y axis at y= 0.75000

y-intercept = 3/4 = 0.75000

When y = 0 the value of x is 3/1 Our line therefore "cuts" the x axis at x= 3.00000

x-intercept = 3/1 = 3.00000

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 0.750 and for x=2.000, the value of y is 0.250. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 0.250 - 0.750 = -0.500 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = -0.500/2.000 = -0.250

Answer 2

-
`(1)/(4)`

Explanation:

The easiest way to find the slope from this equation is to change it into slope-intercept form. To find slope-intercept form solve for y.

First, subtract 4x from both sides

• 16y=-4x+12

Then, divide both sides by 16

• y=-4/16x+12/16

Finally, simplify the equation

• y=-1/4x+3/4

Slope-intercept form is written as y=mx+b. In the equation above m is -1/4, so that is the slope.