find the equation for the line with the given properties. Express in slope intercept form.
Containing points P=(-3,-4) anda Q=(-1,-1)
(y+4)/(x+3) = 3/2
y = 3/2 x + 1/2
To find the equation for the line containing points P=(-3,-4) and Q=(-1,-1), we can use the slope-intercept form of a line equation: y = mx + b. Here, m represents the slope of the line and b represents the y-intercept.
First, we need to find the slope (m) of the line. The slope is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Using the coordinates of points P and Q:
m = (-1 - (-4)) / (-1 - (-3))
m = (3) / (2)
m = 3/2
Now that we have the slope, we can use the coordinates of one of the points (let's use point P: x₁ = -3, y₁ = -4) and the slope to find the y-intercept (b). Rearranging the slope-intercept form:
y = mx + b
-4 = (3/2)(-3) + b
-4 = -9/2 + b
We can now solve for b:
-4 + 9/2 = b
-8/2 + 9/2 = b
1/2 = b
Now we have the slope (m = 3/2) and the y-intercept (b = 1/2), so the equation of the line in slope-intercept form is:
y = (3/2)x + 1/2