The point A has coordinates (-12, -7) and the point B has coordinates (-8 , 1).
Find the equation of the line parallel to AB and passing through (2,5).
Thanks.
slope AB = m = (1+7)/(-8+12) = 8/4 = 2
using (2,5)
y-5 = 2(x-2)
AB has slope (1+7)/(-8+12) = 2
Now you have a point and a slope, so the line is
y-5 = 2(x-2)
shush suck u mum
To find the equation of a line parallel to AB and passing through a given point, we will first find the slope of line AB.
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates of points A and B:
m = (-7 - 1) / (-12 - (-8))
= (-7 - 1) / (-12 + 8)
= (-8) / (-4)
= 2
So the slope of line AB is 2.
Since we want to find a line parallel to AB, the slope of the parallel line will also be 2.
Now, we can use the point-slope form of a linear equation to determine the equation of the line. The point-slope form is given by:
y - y1 = m(x - x1)
Using the point (2, 5) and the slope (m = 2):
y - 5 = 2(x - 2)
Now, we can simplify and rewrite the equation in slope-intercept form (y = mx + b), where b is the y-intercept:
y - 5 = 2x - 4
y = 2x - 4 + 5
y = 2x + 1
Therefore, the equation of the line parallel to AB and passing through the point (2, 5) is y = 2x + 1.