<h3>Answer:</h3>
y = 8/9x + 80/9
<h3>Step-by-step explanation:</h3><u>We are given;</u>
- Equation of a line as 8x -9y -2 = 0
- Coordinates (-1,8)
We are required to determine the equation of a line parallel to the given line and passing through a point (-1,8)
<h3>Step 1: Determine the Gradient of the given line </h3>- When an equation is written in the form y = mx + c, m is the gradient.
- Therefore; we could write the equation 8x -9y -2 = 0 in the form of y= mx + c
9y = 8x -2
y = 8/9x - 2/9
Therefore, the slope, m = 8/9
<h3>Step 2: Determine the equation of the line</h3>- We need to know that parallel lines have the same gradient
- Therefore, the slope of the line in question is 8/9
- It passes through a point (-1, 8)
We can therefore, determine the equation;
Taking another point, (x,y)
9(y-8) = 8(x+1)
9y - 72 = 8x + 8
9y = 8x + 8 +72
9y = 8x + 80
y = 8/9x + 80/9
Therefore, the equation of the line is y = 8/9x + 80/9