Find the equation with the given properties. Express the equation in slope intercept form.
Containing points p=(-4,-2) and Q=(-2,1)
What is the equation of the line?
y=
P(-4,-2), Q(-2,1).
m = (1-(-2))/(-2-(-4)) = 3/2.
Y = mx + b
Y = (3/2)*(-4) + b = -2
-6 + b = -2
b = 4.
Eq: Y = 3x/2 + 4
To find the equation of the line passing through two given points, we can use the slope-intercept form of a linear equation, which is:
y = mx + b
where:
m = slope of the line
b = y-intercept
To find the slope (m), we use the formula:
m = (y2 - y1) / (x2 - x1)
Given the points:
p = (-4, -2) = (x1, y1)
Q = (-2, 1) = (x2, y2)
Substituting these values into the slope formula:
m = (1 - -2) / (-2 - -4)
m = 3 / 2
m = 1.5
Now that we have the slope (m), we can substitute one of the points (p or Q) and the slope (m) into the slope-intercept form to find the y-intercept (b).
Let's use point p (-4, -2):
y = mx + b
-2 = 1.5(-4) + b
-2 = -6 + b
b = -2 + 6
b = 4
Now we have the slope (m = 1.5) and the y-intercept (b = 4), so we can write the equation in slope-intercept form:
y = 1.5x + 4