Answer:
y = 3/4x + 5
-3x + 4y = 20
Step-by-step explanation:
In order to write this equation, you need the slope and y-intercept (I'll answer in slope-intercept form and standard form)
First change that standard form equation to slope-intercept form:
1. 4x + 3y = 8
2. 3y = -4x + 8
3. y = -4/3x + 8/3
Step 1 is given.
In step 2, 4x was subtracted from both sides.
In step 3, both sides were divided by 3.
Slope-intercept form:
y = mx + b
m is the slope and b is the y-intercept.
m = 3/4; the slope of a line perpendicular to another line is the negative reciprocal of the other line's slope (ex: line's slope is 1/4; a line perpendicular to it has a slope of -4, the negative reciprocal)
b = 5; the y-intercept was stated in the problem
Now, you put it together: y = 3/4x + 5
Standard form:
You can just change the slope intercept form back into standard form by moving the numbers around a bit:
1. y = 3/4x + 5
2. -3/4x + y = 5
3. -3x + 4y = 20
Step 1 is given.
In step 2, 3/4x was subtracted from both sides of the equation.
In step 3, both sides were multiplied by 4 so that the equation could have nice whole numbers. (this step is optional, I just think it's easier to read this way)
