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.