Write an equation of the line passing through the points 3,11 and -2, -19
y=1/6x then howd ya do b?
The line through (3,11) and (-2,-19) has slope (-19-11)/(-2-3) = 6
So, its equation is
y-11 = 6(x-3)
or some rearrangement of that.
Not sure just what you're after. What does y = 1/6 x have to do with it?
98
To find the equation of a line passing through two points, we can use the point-slope form of the linear equation, which is:
y - y1 = m(x - x1)
where (x1, y1) represents the coordinates of one point on the line, and m is the slope of the line.
Given the points (3, 11) and (-2, -19), we can find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates, we get:
m = (-19 - 11) / (-2 - 3) = -30 / -5 = 6
So, the slope of the line passing through the two points is 6.
Now, we can substitute one of the points (3, 11) and the slope (m = 6) into the point-slope equation to find the equation of the line:
y - y1 = m(x - x1)
y - 11 = 6(x - 3)
Expanding the equation:
y - 11 = 6x - 18
Rearranging the terms to get the equation in the standard form:
y = 6x - 18 + 11
y = 6x - 7
Therefore, the equation of the line passing through the points (3, 11) and (-2, -19) is y = 6x - 7.
To find the equation of a 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. To determine the slope, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Given the points (3, 11) and (-2, -19), we can substitute the coordinates into the formula:
m = (-19 - 11) / (-2 - 3)
m = (-30) / (-5)
m = 6
Now that we have the slope (m = 6), we can substitute it into the slope-intercept form equation along with one point's coordinates (3, 11):
y = mx + b
11 = 6(3) + b
Solving for b:
11 = 18 + b
11 - 18 = b
-7 = b
So the y-intercept (b) is -7. Therefore, the equation of the line passing through the points (3, 11) and (-2, -19) is:
y = 6x - 7