How do you find the slope and y intercept for: #8x-12y = 24 #?

Question

Savannah Anderson · Accepted Answer

Slope: #2/3#

y-intercept: #(-2)# Given #color(white)("XX")8x-12y=24# #color(white)("XX")12y= 8x-24# #color(white)("XX")y=2/3x+(-2)# which is is "slope-intercept form" (#y=mx+b#) with slope #m=2/3# and y-intercept #= -2#

Julia Adams · Answer

Gradient #+2/3# .......... Intercept #x=0 , y=-2# written as (0,2)

I have provided an 'over the top' explanation to accommodate all levels of comprehension; readers with slightly higher understanding levels will need to weed out certain information! Typically, in mathematics, the whole is divided into elements or parts, and the parts are then solved. Here's what I'll do, step-by-step illustrated so you can see what's going on: There are a few things about this context that need to be understood before we get started. The amount of up that you experience when moving from left to right for the length of the gradient is known as the slope (or gradient). This "amount" of up can be positive or negative; if it is positive, the gradient is actually going upward; if it is negative, the gradient is going downward. According to convention, 1. The values of the variable "y" are indicated by the vertical axis. The variable 'x' is represented by its value on the horizontal axis. Since 'x' can have any value assigned to it, 'y' is dependent on the value of 'x,' making it the dependent variable. On the other hand, 'x' can have any value assigned to it, making it the independent variable. The usual standardised format of this equation type is to write the dependent variable on it's own to the left of the equals sign and everything else to the right. so you would write #8x-12y=24# as: #12y=8x-24 # #y=(8x-24)/12 # # y=2/3x - 2# To find the #y# intercept: The intercept is where the plotted line crosses the #y"-axis"#. In this case it only does it once. The value of the #x"-axis"# at this point is zero. So we may substitute the value of zero for #x# in #y=2/3x-2# giving #y=2/3(0)-2# #y = 0 -2# #y = -2# To find gradient: With this type of context it is simply the coefficient of #x# ( the number in front of it. So for every 1 along the #x#-axis you go upwards #1/3# on the #y#-axis. So the gradient is #(1/3)/1 = 1/3# Since this is positive, the gradient is positive (upwards).

Eva Abramson · Answer

undefined To find the slope and y-intercept for the equation 8x - 12y = 24:

1. Rewrite the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
2. Solve the equation for y to isolate it.
3. Once in slope-intercept form, identify the coefficient of x as the slope, and the constant term as the y-intercept.