Final answer:
The slope of the line represented by the equation 4x - 8y = 12 is 1/2, found by rewriting the equation in slope-intercept form (y = mx + b) and identifying the coefficient of x as the slope.
Step-by-step explanation:
The equation of a line in standard form is given as 4x - 8y = 12, and you want to find the slope of this line. To find the slope from the standard form, the equation needs to be re-written in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Here's how to do it step-by-step:
- First, move the x term to the other side of the equation: -8y = -4x + 12.
- Next, divide every term by -8, the coefficient of y, to isolate y: y = ½x - ÷.
Now, the equation is in slope-intercept form, and the coefficient of x (1/2) is the slope. Therefore, the slope of the line is 1/2. This means that the line rises 1 unit vertically for every 2 units it moves horizontally.