given order pairs (-4,-2) and (-1,-5), develop an equation in the slope intercept format
first solve for the slope (m)
then in the equation in the slope intercept format y=mx+b
m = (-5 -(-2)) / (-1 -(-4)),
m = -3 / 3 = -1.
y = mx €= b,
-2 = (-1)(-4) + b,
-2 = 4 + b,
-6 = b,
b = -6.
Eq: y = -x - 6
CORRECTION:
Y = mx + b.
To find the equation of a line in slope-intercept form (y = mx + b), we need to first find the slope (m) and then find the y-intercept (b).
Given the ordered pairs (-4,-2) and (-1,-5), we can use the slope formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (-4,-2) and (x2, y2) = (-1,-5).
Substituting the values into the formula, we have:
m = (-5 - (-2)) / (-1 - (-4))
= (-5 + 2) / (-1 + 4)
= -3 / 3
= -1
So the slope (m) is -1.
Next, we can use either of the given points to find the y-intercept (b). Let's use the point (-4,-2).
We know that the equation y = mx + b holds true for any point on the line, so we can substitute the coordinates of the point into the equation and solve for b:
-2 = -1*(-4) + b
-2 = 4 + b
b = -2 - 4
b = -6
Therefore, the equation of the line in slope-intercept form is:
y = -x - 6