in slope-intercept form, what is the equation of the line passing through (6,22) and parallel to the line joining (11,3) and (2,6)
The slope of the second line you mentioned is
(y2-y1)/(x2-x1) = (6-3)/(2-11) = -1/3
Therefore you are looking for a line which passes through (6,22) with slope -1/3.
That would be (y - 22) = (-1/3)(x-6)
which can be rewritten
y = (-x/3) + 24
To find the equation of a line in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b).
First, let's find the slope of the line joining (11,3) and (2,6). The slope (m) can be calculated using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line.
Using the coordinates (11,3) and (2,6), the slope (m) is:
m = (6 - 3) / (2 - 11) = 3 / (-9) = -1/3
Since the line we are interested in is parallel to this line, it will have the same slope.
Now, we have the slope (m = -1/3) and the point (6,22) that the line passes through. We can use the point-slope form of a line to find the equation: y - y1 = m(x - x1).
Let's substitute the values:
y - 22 = (-1/3)(x - 6)
Now, let's simplify the equation:
y - 22 = (-1/3)x + 2
To convert the equation to slope-intercept form, we need to isolate y:
y = (-1/3)x + 2 + 22
y = (-1/3)x + 24
Therefore, the equation of the line passing through (6,22) and parallel to the line joining (11,3) and (2,6) is y = (-1/3)x + 24 in slope-intercept form.