Write the equation, in slope-intercept form if possible, of the line passing through the two points.
(1,4) and (6,4)
To find the equation of the line passing through two points, we can use the slope-intercept form,
y = mx + b
where m is the slope of the line and b is the y-intercept.
First, let's find the slope (m) using the two given points.
m = (y2 - y1) / (x2 - x1)
Using the points (1, 4) and (6, 4):
m = (4 - 4) / (6 - 1)
m = 0 / 5
m = 0
Now that we have the slope (m = 0), we can substitute it into the slope-intercept form to find the y-intercept (b).
Using one of the given points, let's use (1, 4):
4 = 0*1 + b
4 = b
Since b = 4, the equation of the line passing through the points (1, 4) and (6, 4) is:
y = 0x + 4
Simplifying:
y = 4
To find the equation of the line passing through two points, we use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (1, 4) and (6, 4), we substitute the values into the formula:
m = (4 - 4) / (6 - 1)
m = 0 / 5
m = 0
Since the slope (m) is 0, we can write the equation as y = b.
To find the y-intercept (b), we can choose any of the given points (1, 4) or (6, 4) and substitute the values into the equation.
Using the point (1, 4), we have:
4 = b
So the y-intercept (b) is 4.
Therefore, the equation of the line passing through the points (1, 4) and (6, 4) is y = 4.
To find the equation of a line passing through two given points, we can use the slope-intercept form of a linear equation, which is given by:
y = mx + b
where m is the slope of the line and b is the y-intercept.
To find the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Let's substitute the coordinates of the two given points into the formula:
m = (4 - 4) / (6 - 1)
m = 0 / 5
m = 0
Since the slope (m) is 0, the equation of the line will have the form:
y = bx + c
To find the y-intercept (c), we can substitute the coordinates of one of the given points into the equation:
4 = b * 1 + c
Since the line passes through the point (1, 4), we can substitute these values into the equation:
4 = b * 1 + c
Simplifying the equation, we have:
4 = b + c
To find the value of c, we need more information. Since the slope (m) is 0, the line will be a horizontal line. We know that a horizontal line has a constant y-value (vertical line) and does not depend on the x-value. In this case, the y-value is 4. Therefore, we can conclude that b = 0 and c = 4.
Now that we know the values of b and c, we can write the final equation in slope-intercept form:
y = 0x + 4
Simplifying further, we have:
y = 4
So, the equation of the line passing through the points (1, 4) and (6, 4) is y = 4.