What is an equation of the line that passes through the points left bracket, 4, comma, minus, 3, right bracket(4,−3) and left bracket, 2, comma, minus, 4, right bracket(2,−4)?
To find the equation of a line passing through two points, we need to determine the slope-intercept form of the equation, which is in the form y = mx + b, where m is the slope and b is the y-intercept.
First, we need to find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (4, -3) and (2, -4), we have:
m = (-4 - (-3)) / (2 - 4)
m = (-4 + 3) / (2 - 4)
m = -1 / (-2)
m = 1/2
Now that we have the slope (m = 1/2), we can substitute this and one of the points into the slope-intercept form to find b:
y = mx + b
-3 = (1/2)(4) + b
-3 = 2 + b
b = -3 - 2
b = -5
Thus, the equation of the line passing through the points (4, -3) and (2, -4) is:
y = (1/2)x - 5
To find the equation of the line that passes through the points (4, -3) and (2, -4), we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1).
First, let's find the slope (m). The slope (m) is given by the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
Using the given points (4, -3) and (2, -4), we have:
m = (-4 - (-3)) / (2 - 4)
m = (-4 + 3) / (2 - 4)
m = -1 / (-2)
m = 1/2
Now that we have the slope, we can choose either of the two points to substitute into the point-slope form. Let's use the point (4, -3):
y - (-3) = 1/2(x - 4)
y + 3 = 1/2x - 2
y = 1/2x - 2 - 3
y = 1/2x - 5
Therefore, the equation of the line that passes through the points (4, -3) and (2, -4) is y = 1/2x - 5.
To find the equation of the line that passes through two given points, we can use the slope-intercept form of a linear equation: y = mx + b, where m represents the slope of the line and b represents the y-intercept.
Step 1: Find the slope (m)
The slope (m) of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Given the points (4, -3) and (2, -4), we can substitute the values into the formula:
m = (-4 - (-3)) / (2 - 4)
m = (-4 + 3) / (-2)
m = -1 / -2
m = 1/2
Step 2: Find the y-intercept (b)
To find the y-intercept (b), we can use one of the given points and substitute its coordinates into the slope-intercept equation (y = mx + b). Let's use the point (4, -3).
-3 = (1/2)(4) + b
-3 = 2 + b
b = -3 - 2
b = -5
So, the y-intercept (b) is -5.
Step 3: Write the equation
Now that we have determined the slope (m = 1/2) and the y-intercept (b = -5), we can write the equation of the line:
y = (1/2)x - 5
Therefore, the equation of the line that passes through the points (4, -3) and (2, -4) is y = (1/2)x - 5.