Write the equation, in slope-intercept form if possible, of the line passing through the two points.
(8,3) and (8,−6)
When the x-coordinates of two points are the same, it means that the line passing through those points will be vertical. In this case, the x-coordinate of both points is 8, so the line is vertical.
A vertical line does not have a well-defined slope, so it cannot be expressed in slope-intercept form (y = mx + b).
The equation of the vertical line passing through these two points is simply x = 8.
To find the equation of the line passing through two points, we need to find the slope and the y-intercept.
Given points: (8, 3) and (8, -6), we can see that both points have the same x-coordinate of 8.
Since the slope of a vertical line is undefined, we can't find the slope using the formula (y2 - y1) / (x2 - x1) in this case.
However, we can still write the equation in slope-intercept form by recognizing that the line is vertical, passing through the point (8, 3).
The equation of a vertical line in slope-intercept form is x = constant.
In this case, the x-coordinate is always 8. Hence, the equation of the line passing through the points (8, 3) and (8, -6) is:
x = 8
To find the equation of a line passing through two given points, you can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope of the line and b is the y-intercept.
In this case, we have two points: (8, 3) and (8, -6). Since both points have the same x-coordinate, the line is vertical and has an undefined slope.
To determine the equation, we need to find the x-value that remains constant for any y-value. In this case, it is x = 8. Therefore, the equation of the line is simply x = 8, which is the equation of a vertical line passing through the x-coordinate 8.
Note that in slope-intercept form, the equation would be in the form y = mx + b. However, for a vertical line, the slope (m) is undefined, so the slope-intercept form cannot be applied. Instead, we use the equation x = 8 to represent the vertical line passing through the point (8, 3) and (8, -6).