Answer:
y = -4/9x + 3
Explanation:
Keep in mind:
- the equation for slope-intercept form is y = mx + b.
- "y" means output, "x" means input, "m" means slope, and "b" means y intercept
The first step in this equation is to turn 9x - 4y = -8 into slope intercept form.
Step 1: subtract 9x from both sides to begin to isolate y.
9x - 4y = -8
-4y = -9x - 8
Step 2: divide both sides by -4 to further isolate y.
y = 9/4x + 2
Now, we have the equation for the perpendicular line. Remember, the slope of a line is the opposite reciprocal of the slope of the line perpendicular to it.
This means that the slope of the line we are trying to find the equation for is -4/9.
Now that we have a slope and a point the line passes through, (0, 3), we can find the equation. Plug the coordinates of the point and the slope into the equation for slope-intercept form.
3 = -4/9(0) + b
To find the equation, solve for b.
Step 1: Simplify -4/9(0)
3 = 0 + b
Step 2: Simplify 0 + b
3 = b
Now that we know b and m, we have our equation.
The final answer is y = -4/9x + 3.