What is an equation of the line that passes through the points left bracket, minus, 5, comma, 0, right bracket
(
−
5
,
0
)
(−5,0) and left bracket, minus, 2, comma, minus, 3, right bracket
(
−
2
,
−
3
)
(−2,−3)?
To find the equation of the line passing through two points, we can use the point-slope form of a line, which is given by:
y - y1 = m(x - x1)
where (x1, y1) are the coordinates of one point on the line, and m is the slope of the line.
First, let's find the slope (m) of the line passing through the two points:
m = (change in y) / (change in x)
= (-3 - 0) / (-2 - (-5))
= (-3 - 0) / (-2 + 5)
= -3 / 3
= -1
Now that we have the slope, we can choose one of the given points (in this case, let's use (-5, 0)) and substitute the values into the point-slope form:
y - 0 = -1(x - (-5))
y = -x + 5
Therefore, the equation of the line passing through the points (-5, 0) and (-2, -3) is y = -x + 5.
To find the equation of the line that passes through the points (-5, 0) and (-2, -3), we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
First, we'll find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1). Let's label the points as follows:
Point 1: (-5, 0)
Point 2: (-2, -3)
Substituting the values into the formula:
m = (-3 - 0) / (-2 - (-5))
m = (-3 - 0) / (-2 + 5)
m = -3 / 3
m = -1
So the slope (m) is -1.
Next, we can choose one of the points and substitute its coordinates into the equation y = mx + b to solve for the y-intercept (b). Let's use point 2 (-2, -3):
-3 = -1 * -2 + b
-3 = 2 + b
b = -3 - 2
b = -5
So the y-intercept (b) is -5.
Therefore, the equation of the line that passes through the given points is:
y = -x - 5
To find the equation of a line passing through two given points, we can use the point-slope form of the equation. The point-slope form is given by:
y - y1 = m(x - x1)
where (x1, y1) are the coordinates of one of the points on the line and 'm' is the slope of the line.
First, let's find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates of the given points into the formula:
m = (-3 - 0) / (-2 - (-5))
= (-3) / (3)
= -1
Now that we have the slope (m = -1), we can choose either of the given points on the line (let's use (-5, 0)) and substitute its coordinates into the point-slope form:
y - y1 = m(x - x1)
y - 0 = -1(x - (-5))
y = -x + 5
Therefore, the equation of the line passing through the points (-5, 0) and (-2, -3) is y = -x + 5.