What is an equation of the line that passes through the points left bracket, 6, comma, 4, right bracket(6,4) and left bracket, minus, 5, comma, 4, right bracket(−5,4)?
To find the equation of the line that passes through the given points, we need to determine the slope and the y-intercept.
The slope (m) of a line passing through two points (x1,y1) and (x2,y2) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
So in this case, the slope (m) is:
m = (4 - 4) / (-5 - 6) = 0 / -11 = 0
Since the y-coordinate of both points is 4, the line is parallel to the x-axis, and therefore, the slope is 0.
Now that we have the slope (m), we can proceed to find the y-intercept.
Using the point-slope form of a line, which is y - y1 = m(x - x1), where (x1,y1) is any point on the line, we substitute the values of one of the points (6,4):
y - 4 = 0(x - 6)
y - 4 = 0
y = 4
So the equation of the line is y = 4.
To find the equation of a line that passes through two points, you can use the slope-intercept form of a linear equation: y = mx + b, where m represents the slope and b represents the y-intercept.
Step 1: Find the slope (m)
The formula for calculating the slope (m) between two points (x1, y1) and (x2, y2) is: m = (y2 - y1) / (x2 - x1).
Let's find the slope using the given points (6,4) and (-5,4):
m = (4 - 4) / (-5 - 6)
m = 0 / -11
m = 0
Step 2: Substitute one of the points and the slope into the equation
Since the slope (m) is 0, the equation will be in the form y = b, where b is the y-intercept. We can choose any point to substitute into the equation.
Let's use the point (6,4):
4 = 0 * 6 + b
4 = 0 + b
4 = b
Step 3: Write the equation
Using the y-intercept (b) we found in Step 2, the equation of the line passing through the points (6,4) and (-5,4) is given by:
y = 4
So, the equation of the line is y = 4.
To find the equation of a line that passes through two given points, follow these steps:
Step 1: Find the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Let's label the coordinates of the points as follows:
Point 1: (x1, y1) = (6, 4)
Point 2: (x2, y2) = (-5, 4)
Using the formula, the slope is:
m = (4 - 4) / (-5 - 6)
= 0 / -11
= 0
Since the numerator is zero, the line is horizontal, and the slope is zero.
Step 2: Write the equation of the line using the slope-intercept form: y = mx + b
In this case, the slope (m) is 0. Substituting the values into the equation, we have:
y = 0x + b
y = b
So the equation of the line is y = 4.
Since the slope is zero, the line is a horizontal line passing through the y-axis at y = 4.