Question 6
Find an equation for the line that passes through the points (-6,-5) and (4,-1)
To find the equation for the line that passes through the points (-6,-5) and (4,-1), we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where (x1, y1) are the coordinates of one of the points, and m is the slope of the line.
First, let's find the slope (m). The formula to find the slope between two points (x1, y1) and (x2, y2) is:
m = (y2 - y1)/(x2 - x1)
Using the points (-6,-5) and (4,-1):
m = (-1 - (-5))/(4 - (-6))
= (4)/(10)
= 2/5
So the slope (m) is 2/5.
Now, let's choose one of the points to put into the point-slope form. We'll use the point (-6,-5), so x1 = -6 and y1 = -5.
Plugging in the values into the point-slope form:
y - (-5) = (2/5)(x - (-6))
y + 5 = (2/5)(x + 6)
y + 5 = (2/5)x + (2/5)(6)
y + 5 = (2/5)x + 12/5
Finally, we can simplify the equation:
y + 5 = (2/5)x + 12/5
y = (2/5)x + 12/5 - 5
y = (2/5)x + 12/5 - 25/5
y = (2/5)x - 13/5
Therefore, the equation for the line that passes through the points (-6,-5) and (4,-1) is y = (2/5)x - 13/5.