Given that the points (16, −5) and (−40, 16) lie on a line, what is the equation of the line? Select two answers.
A.
y=−38x+1
B.
y=−83x+1
C.
y+5=−38(x−16)
D.
y+5=−83(x−16)
For the points you gave, the slope is - 21/-56 or -3/8
None of your choices show that slope
In C, did you mean
y+5=−3/8(x−16)
If so, it would be a correct choice.
To find the equation of a line, we can use the formula:
y - y1 = m(x - x1),
where (x1, y1) is a point on the line and m is the slope of the line.
Given the points (16, -5) and (-40, 16), we can find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1),
where (x1, y1) = (16, -5) and (x2, y2) = (-40, 16).
m = (16 - (-5)) / (-40 - 16) = 21 / (-56).
Simplifying the slope, we get:
m = -21 / 56 = -3 / 8.
Now, using the point-slope formula, we can find the equation of the line:
y - y1 = m(x - x1),
where (x1, y1) = (16, -5) and m = -3 / 8.
Plugging in the values, we have:
y - (-5) = (-3 / 8)(x - 16).
Simplifying the equation, we get:
y + 5 = (-3 / 8)(x - 16).
Rearranging the equation, we have:
8(y + 5) = -3(x - 16).
Expanding and simplifying, we get:
8y + 40 = -3x + 48.
Rearranging the equation, we have:
3x + 8y = 8.
Therefore, the equation of the line is:
3x + 8y = 8.
However, this equation is not among the answer choices provided. Therefore, the correct answer is none of the above.
To find the equation of a line given two points, we can use the slope-intercept form of a line: y = mx + b, where m is the slope of the line and b is the y-intercept.
First, we need to find the slope of the line using the given points. The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
Using the points (16, -5) and (-40, 16), we can calculate the slope:
m = (16 - (-5)) / (-40 - 16) = 21 / -56 = -3 / 8
Now that we have the slope (m = -3/8), we can substitute it into the slope-intercept form:
y = (-3/8)x + b
To find the y-intercept (b), we can use one of the given points. Let's use the point (16, -5). Substituting these values into the equation, we have:
-5 = (-3/8)(16) + b
-5 = -6 + b
b = 1
So the equation of the line is:
y = (-3/8)x + 1
Looking at the provided answer choices, the correct options are:
A. y = -38x + 1
C. y + 5 = -38(x - 16)