The line through (2, 5), perpendicular to y = -7/3x-1
Question: Write an equation in slope intercept form.
if perpendicular than the slope is
+ 3/7
because it has to be -1/slope of original.
so
It has to look like
y = (3/7) x + b
now put that point in to find b
5 = (3/7) (2) + b
To write an equation in slope-intercept form for the line passing through (2, 5) and perpendicular to the line y = -7/3x - 1, we need to determine the slope of the given line and calculate the negative reciprocal to find the slope of the perpendicular line.
The slope-intercept form of a line is y = mx + b, where m represents the slope and b represents the y-intercept.
In the given equation y = -7/3x - 1, the slope (m) is -7/3.
To find the slope of the perpendicular line, we need to calculate the negative reciprocal of -7/3.
Reciprocal of -7/3 = -3/7
Negative reciprocal of -3/7 = 3/7.
So, the slope of the line perpendicular to y = -7/3x - 1 is 3/7.
Now, we have the slope (m = 3/7) and a point (2, 5) that lies on the line.
Using the point-slope form of a line: y - y1 = m(x - x1), we can substitute the given values to find the equation.
Using (x1, y1) = (2, 5) and m = 3/7:
y - 5 = 3/7(x - 2)
To convert the equation to slope-intercept form, we need to simplify it.
y - 5 = 3/7x - 6/7
Rearranging the terms, we get:
y = 3/7x - 6/7 + 5
y = 3/7x - 6/7 + 35/7
Combining the constants, the equation in slope-intercept form is:
y = 3/7x + 29/7
To find the equation of a line perpendicular to a given line, we need to determine the slope of the given line first.
The given line has a slope of -7/3.
Since the line perpendicular to the given line will have a negative reciprocal slope, we can find the perpendicular slope by flipping the fraction and changing the sign. Therefore, the perpendicular slope is 3/7.
Now, we can use the point-slope form of a linear equation to find the equation of the line. The point-slope form is:
y - y₁ = m(x - x₁)
Where (x₁, y₁) is the given point, and m is the slope.
Plugging in the values (2, 5) for (x₁, y₁) and 3/7 for m, we get:
y - 5 = (3/7)(x - 2)
To convert this equation to slope-intercept form (y = mx + b), we can distribute (3/7) to (x - 2) and rearrange the equation:
y - 5 = (3/7)x - 6/7
Adding 5 to both sides of the equation, we have:
y = (3/7)x - 6/7 + 5
Simplifying further:
y = (3/7)x - 6/7 + 35/7
Combining the fractions:
y = (3/7)x + 29/7
Therefore, the equation of the line through (2, 5) and perpendicular to y = -7/3x - 1 is y = (3/7)x + 29/7.