For each exercise below, find the equation of the line passing through the given points. Circle the two letters next to the correct equation. Then write these letters in the two boxes at the bottom of the page that contain the number of that exercise.
(3, -1) (-6, -4)
To find the equation of the line passing through the two given points, we can use the point-slope form of a linear equation.
Point-slope form:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line, and m is the slope of the line.
Let's find the slope first:
m = (y2 - y1) / (x2 - x1)
Using the points (3, -1) and (-6, -4):
m = (-4 - (-1)) / (-6 - 3)
m = (-4 + 1) / (-6 - 3)
m = -3 / -9
m = 1/3
Now that we have the slope, we can choose one of the given points (let's choose (3, -1)) and substitute the values into the point-slope form:
y - (-1) = (1/3)(x - 3)
y + 1 = (1/3)(x - 3)
Now, let's simplify this equation:
y + 1 = (1/3)x - 1
y = (1/3)x - 2
The equation of the line passing through the points (3, -1) and (-6, -4) is y = (1/3)x - 2.
The correct equation is "y = (1/3)x - 2". The corresponding letters are "C" and "F".
So, the two boxes at the bottom of the page contain the letters "C" and "F".