Answer:
a. y = 8x + 7
b. 8y = -x-74
Explanation:
Here, we want to write the equation of a line which is parallel to y = 8x + 7 and passes through the given point
Since the line we want to write the equation is parallel to y = 8x + 7, it means that they have the same slope
Mathematically we can write the equation of a line as y = mx + c where m is the slope. Comparing this with y = 8x + 7, our slope is therefore 8
Now, the slope of our new line is also 8
We now make use of the point slope method to write the equation
Mathematically the point slope method is;
y-y1 = m(x-x1)
where our (x1,y1) = (-2,-9)
y-(-9) = 8(x -(-2))
y + 9 = 8(x + 2)
y + 9 = 8x + 16
y = 8x + 16-9
y = 8x + 7
For the second line, it is perpendicular to y = 8x + 7
Here too, we have the slope as 8
Now since they are perpendicular, it means that the product of the slopes is equal to -1
m1 * m2 = -1
8 * m2 = -1
m2 = -1/8
Now;
y-y1 = m(x-x1)
our point still remains same (-2,-9)
y-(-9) = -1/8 (x -(-2))
y + 9 = -1/8(x + 2)
8(y + 9) = -1(x + 2)
8y + 72 = -x -2
8y = -x -2-72
8y = -x-74