Which equation is the equation of a line that passes through (-10, 3) and is perpendicular to y=5x-7?
a. y=5x +53
b.y=-1/5 x -7
c. y=-1/5x+1
d. y=1/5x +5.
so the new line must be y = (-1/5)x + b
which automatically rules out a) and d)
plug in the point (-10,3) and find b to decide which of the remaining choices is it.
To find the equation of a line that is perpendicular to another line, you need to determine the slope of the given line and then find the negative reciprocal of that slope.
The given line, y = 5x - 7, has a slope of 5 (since it is in the form y = mx + b, where m is the slope).
The negative reciprocal of 5 is -1/5.
So, the equation of the line that is perpendicular to y = 5x - 7 and passes through (-10, 3) is:
y = -1/5x + b
Now we need to find the value of b.
Substituting the coordinates (-10, 3) into the equation, we get:
3 = -1/5(-10) + b
Simplifying this equation, we have:
3 = 2 + b
Subtracting 2 from both sides, we get:
1 = b
Therefore, the equation of the line is:
y = -1/5x + 1
So, the correct answer is c. y = -1/5x + 1.
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.
First, let's determine the slope of the given line, y = 5x - 7. In this equation, the coefficient of x, which is 5, represents the slope. Therefore, the slope of the given line is 5.
Next, we need to find the negative reciprocal of 5. The negative reciprocal of a number is the number obtained by flipping the fraction and changing the sign.
So, the negative reciprocal of 5 is -1/5.
Now, we have the slope of the line that is perpendicular to the given line.
The equation of a line can be written in the form y = mx + b, where m is the slope and b is the y-intercept.
Using the point (-10, 3), we can substitute the coordinates into the equation y = mx + b to solve for the y-intercept, b.
3 = (-1/5)(-10) + b
3 = 2 + b
b = 3 - 2
b = 1
Now that we have the slope (-1/5) and the y-intercept (1), we can write the equation of the line as y = -1/5x + 1.
Therefore, the correct answer is c. y = -1/5x + 1.