Write an equation in standard form for a line passing through the pair of points.
(5,3) and (-3,-8)
1. find the slope
2. pick one of the points, I would pick (5,3) and use it in
(y-3) = slope(x-5)
simplify and arrange into the form you need.
To write an equation in standard form for a line passing through a pair of points, you can use the point-slope form equation, which is:
y - y1 = m(x - x1)
Where (x1, y1) is one of the given points, and m is the slope of the line.
First, let's find the slope of the line using the given points (5,3) and (-3,-8):
slope (m) = (y2 - y1) / (x2 - x1)
= (-8 - 3) / (-3 - 5)
= (-8 - 3) / (-8)
= -11 / (-8)
= 11 / 8
Now that we have the slope, we can choose one of the given points, say (5,3), and substitute the values into the point-slope form equation:
y - y1 = m(x - x1)
y - 3 = (11/8)(x - 5)
y - 3 = (11/8)x - 11/8 * 5
y - 3 = (11/8)x - 55/8
Next, we can simplify the equation:
8(y - 3) = 11x - 55
8y - 24 = 11x - 55
11x - 8y = 55 - 24
11x - 8y = 31
So the equation in standard form for the line passing through the points (5,3) and (-3,-8) is:
11x - 8y = 31