Write an equation in slope intercept form that is perpendicular to y= -7x -8 and goes through the point (0,9).
(PLEASE SHOW WORK).
start with the point-slope form:
y-9 = 1/7 (x-0)
To find the equation of a line that is perpendicular to a given line, we need to determine the slope of the given line and then find the negative reciprocal of that slope.
Given line: y = -7x - 8
The slope of this line is -7. To find the negative reciprocal of -7, we flip the fraction and change the sign:
Negative reciprocal slope = -1/(-7) = 1/7
So, the slope of the line perpendicular to y = -7x - 8 is 1/7.
Next, we can use the point-slope form of a line to find the equation of the line passing through the point (0,9) with a slope of 1/7:
y - y1 = m(x - x1)
where (x1, y1) represents the coordinates of the given point, and m represents the slope.
Substituting the values, we have:
y - 9 = (1/7)(x - 0)
Simplifying:
y - 9 = 1/7 * x
y - 9 = 1/7x
Finally, let's rewrite the equation in slope-intercept form (y = mx + b) by moving the constant term (-9) to the other side:
y = 1/7x + 9
Therefore, the equation of the line that is perpendicular to y = -7x - 8 and passes through the point (0,9) is y = 1/7x + 9.
To find an equation in slope-intercept form that is perpendicular to y = -7x - 8 and passes through the point (0,9), we need to follow these steps:
Step 1: Determine the slope of the given equation.
In the equation y = -7x - 8, we can see that the slope coefficient (the number multiplying x) is -7. The slope of this equation is -7.
Step 2: Determine the slope of the perpendicular line.
For two lines to be perpendicular, their slopes must be negative reciprocals of each other. So, the perpendicular line will have a slope that is the negative reciprocal of -7.
To find the negative reciprocal, we take the reciprocal of -7, which is -1/7, and then multiply it by -1 to make it negative.
Therefore, the slope of the perpendicular line is 1/7.
Step 3: Use the point-slope form of the equation to write the equation.
The point-slope form of an equation is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope.
Using the coordinates of the given point (0,9), the equation becomes y - 9 = (1/7)(x - 0).
Step 4: Simplify the equation.
Distributing the slope (1/7) to the x term, the equation becomes y - 9 = (1/7)x - 0.
Simplifying further, we have y - 9 = (1/7)x.
To write the equation in slope-intercept form (y = mx + b), we isolate y. Adding 9 to both sides, we get y = (1/7)x + 9.
Therefore, the equation in slope-intercept form that is perpendicular to y = -7x - 8 and passes through the point (0,9) is y = (1/7)x + 9.