What is an equation of the line that passes through the points left bracket, 8, comma, 1, right bracket(8,1) and left bracket, 4, comma, 1, right bracket(4,1)?
The line passing through (8,1) and (4,1) is a horizontal line because the y-coordinates of both points are the same.
The equation of a horizontal line is in the form y = c, where c is the y-coordinate.
Since both points have a y-coordinate of 1, the equation of the line is y = 1.
To find the equation of a line that passes through two points (x1, y1) and (x2, y2), you can use the slope-intercept form of a linear equation: y = mx + b.
First, calculate the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
In this case, the points are (8, 1) and (4, 1), so the slope is:
m = (1 - 1) / (4 - 8) = 0 / -4 = 0
Since the line is horizontal, the slope is 0.
Now, substitute one of the points into the slope-intercept form to find the y-intercept (b). Let's use the point (8, 1):
1 = 0 * 8 + b
1 = b
So the y-intercept (b) is 1.
Therefore, the equation of the line that passes through the points (8, 1) and (4, 1) is:
y = 0x + 1
or simply,
y = 1
To find the equation of a 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 and b represents the y-intercept.
In this case, since both points have the same y-coordinate of 1, the line is a horizontal line. Since a horizontal line has a slope of 0, we can determine the equation of the line.
The equation of the line passing through (8,1) and (4,1) will have the form y = 1x + b. Since the y-intercept is 1 (as both points lie on the line at y = 1), the equation simplifies to y = 1.
Therefore, the equation of the line passing through the points (8,1) and (4,1) is simply y = 1.