Question

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)?

Answer 1

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.