Write an equation of the line containing the given point and parallel to the given line. Express in y=mx+b. (-4, 9); 9x = 8y+5
I attempted this one. I would reverse to y = mx+b; So y = -9x+5. The slope is -9. I would then (y-y^1=m(x-x^1).
y - 9= 1/9(x-5)
Y = 1/9x+45/9. This is still wrong.
(-4 , 9), STD Form: 9x - 8y = 5.
m = -a/b = -9/-8 = 9/8.
y = mx + b = 9,
(9/8)*(-4) + b = 9,
-36/8 + b = 9,
-9/2 + b = 9,
b = 9 + 9/2,
b = 27/2.
Eq: y = (9/8)x + 27/2.
To find the equation of a line parallel to a given line, we need to know that parallel lines have the same slope. In this case, the given line is in the form 9x = 8y + 5.
To convert the given equation into the slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept, we need to isolate y.
Starting with the equation:
9x = 8y + 5
Subtract 5 from both sides:
9x - 5 = 8y
Next, divide both sides by 8 to solve for y:
(9x - 5) / 8 = y
Now we have the equation in the form: y = (9/8)x - 5/8
Since we want a line parallel to this given line, the slope of the new line will also be (9/8).
Using the point-slope form of a linear equation, where (x1, y1) represents the given point, and m represents the slope, we can substitute the values to get the equation in slope-intercept form.
The given point is (-4, 9), so x1 = -4 and y1 = 9.
Putting it all together, the equation of the line parallel to 9x = 8y + 5 and passing through the point (-4, 9) is:
y = (9/8)x + b
To find the y-intercept (b), we substitute the coordinates of the point (-4, 9) into the equation and solve for b:
9 = (9/8)(-4) + b
First, multiply (9/8)(-4):
9 = -36/8 + b
Next, simplify -36/8:
9 = -9/2 + b
To eliminate the fraction, multiply every term by 2:
18 = -9 + 2b
Add 9 to both sides:
27 = 2b
Finally, divide by 2:
b = 27/2
Therefore, the equation of the line parallel to 9x = 8y + 5 and passing through the point (-4, 9) is:
y = (9/8)x + 27/2