What is an equation of the line that passes through the points left bracket, minus, 5, comma, 1, right bracket
(
−
5
,
1
)
(−5,1) and left bracket, 5, comma, minus, 3, right bracket
(
5
,
−
3
)
(5,−3)?
To find the equation of the line that passes through the given points, we first need to find the slope of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (-5, 1) and (5, -3), we can substitute the values into the formula:
m = (-3 - 1) / (5 - (-5))
m = (-4) / 10
m = -2/5
Now that we have the slope, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
Using the first point (-5, 1), we can substitute the values into the equation:
y - 1 = (-2/5)(x - (-5))
y - 1 = (-2/5)(x + 5)
y - 1 = (-2/5)x - 2
y = (-2/5)x - 1
So, the equation of the line that passes through the points (-5, 1) and (5, -3) is y = (-2/5)x - 1.
To find the equation of a line that passes through two points, we can use the point-slope formula. The formula is:
y - y1 = m(x - x1),
where (x1, y1) is one point on the line, and m is the slope of the line.
Let's find the slope (m) first using the formula:
m = (y2 - y1)/(x2 - x1),
where (x1, y1) are the coordinates of the first point and (x2, y2) are the coordinates of the second point.
Given the points (-5, 1) and (5, -3):
m = (-3 - 1)/(5 - (-5))
= -4/10
= -2/5
Now, we have the slope (m) as -2/5. Let's use one of the points (let's use (-5, 1)) and the slope to find the equation.
Using point-slope form:
y - y1 = m(x - x1),
where (x1, y1) = (-5, 1) and m = -2/5:
y - 1 = (-2/5)(x - (-5))
y - 1 = (-2/5)(x + 5)
y - 1 = (-2/5)x - 2
y = (-2/5)x - 2 + 1
y = (-2/5)x - 1
Therefore, the equation of the line that passes through the points (-5, 1) and (5, -3) is y = (-2/5)x - 1.
To find the equation of the line that passes through the given points, we can use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1)
where (x1, y1) is one of the given points and m is the slope of the line.
First, let's calculate the slope (m):
m = (y2 - y1) / (x2 - x1)
Using the coordinates of the given points, we have:
m = (-3 - 1) / (5 - (-5))
m = -4 / 10
m = -2/5
Now that we have the slope, we can choose one of the points (let's use (-5, 1)) and substitute its coordinates into the point-slope form to get the equation of the line:
y - 1 = (-2/5)(x - (-5))
y - 1 = (-2/5)(x + 5)
y - 1 = (-2/5)x - 2
y = (-2/5)x - 1
Therefore, the equation of the line that passes through the points (-5, 1) and (5, -3) is y = (-2/5)x - 1.