Put the following equation of a line into slope-intercept form, simplifying all fractions.
8, x, plus, 12, y, equals, minus, 96
8x+12y=
−96
To put the equation of a line into slope-intercept form (y = mx+b), we need to solve for y, where m is the slope, and b is the y-intercept. The slope-intercept form makes it easy to graph the line.
Given the equation:
8x + 12y = -96
First, we isolate the y-term on one side by subtracting 8x from both sides of the equation:
12y = -8x - 96
Next, we divide the entire equation by 12 to solve for y:
y = (-8x/12) - (96/12)
Simplify both fractions:
-8 and 12 have a common factor of 4, so we can simplify -8/12 to -2/3:
y = (-2/3)x
96 is divisible by 12, and when divided we get -8:
y = (-2/3)x - 8
Now the equation is in slope-intercept form:
y = (-2/3)x - 8
The slope (m) is -2/3, and the y-intercept (b) is -8.