Help me solve (-9,8) and perpendicular to the line whose equation is y=5/6x+7/6
your given line has slope 5/6
so all perpendicular lines have slope -6/5
Now you have a point and a slope, so just use the point-slope form for your new line.
m1 = 5/6.
m2 = -6/5.
P(-9, 8).
Y = m2*x + b,
8 = (-6/5)(-9) + b,
b = ?.
Eq: m2*x + b.
To find the equation of the line perpendicular to y=(5/6)x+(7/6) and passing through (-9,8), we can follow these steps:
Step 1: Determine the slope of the given line.
The equation y=(5/6)x+(7/6) is in slope-intercept form (y=mx+b), where m is the slope. Comparing the equation to the standard form, we can see that the slope of the given line is 5/6.
Step 2: Find the slope of the perpendicular line.
Since a line perpendicular to another line has a slope equal to the negative reciprocal of the slope of the original line, we need to find the negative reciprocal of 5/6. The negative reciprocal of 5/6 is -6/5.
Step 3: Use the point-slope form to write the equation.
The point-slope form of a line is y-y1 = m(x-x1), where (x1, y1) is a point on the line and m is the slope of the line.
We can substitute the values (-9,8) for (x1, y1) and -6/5 for m to write the equation as:
y - 8 = (-6/5)(x - (-9))
Step 4: Simplify the equation.
First, distribute (-6/5) to (x - (-9)) to get:
y - 8 = (-6/5)(x + 9)
This can be further simplified by multiplying -6/5 by each term inside the parentheses:
y - 8 = (-6/5)x - (6/5) * 9
y - 8 = (-6/5)x - 54/5
Step 5: Rearrange the equation into slope-intercept form.
To convert the equation into slope-intercept form (y=mx+b), we can add 8 to both sides of the equation:
y = (-6/5)x - 54/5 + 8
Simplifying further:
y = (-6/5)x - 54/5 + 40/5
y = (-6/5)x - 14/5
Therefore, the equation of the line perpendicular to y=(5/6)x+(7/6) and passing through (-9,8) is y=(-6/5)x - 14/5.
To solve the problem, we need to find the equation of the line perpendicular to the given line and passing through the point (-9, 8).
Step 1: Find the slope of the given line.
The equation of the given line is y = (5/6)x + (7/6).
The coefficient of x is the slope of the line. So, the slope of the given line is 5/6.
Step 2: Find the slope of the line perpendicular to the given line.
Two lines are perpendicular to each other when the product of their slopes is -1. Therefore, the slope of the line perpendicular to the given line is the negative reciprocal of the slope of the given line.
The slope of the line perpendicular to the given line = -1 / (5/6)
= -6/5
Step 3: Use the point-slope form of a line to find the equation of the line.
The point-slope form of a line is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Using the point (-9, 8) and the slope -6/5, we can write the equation as:
y - 8 = (-6/5)(x - (-9))
Simplifying, we have:
y - 8 = (-6/5)(x + 9)
To express the equation in the slope-intercept form (y = mx + b), where b is the y-intercept, we can continue simplifying:
y - 8 = (-6/5)x - 54/5
y = (-6/5)x - 54/5 + 40/5
y = (-6/5)x - 14/5
Therefore, the equation of the line perpendicular to the given line and passing through the point (-9, 8) is y = (-6/5)x - 14/5.