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
(-1, 2) (3, 4)
To find the equation of the line passing through the given points (-1, 2) and (3, 4), we can use the slope-intercept form of a linear equation: y = mx + b.
Step 1: Find the slope (m) of the line.
The slope (m) is given by the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the given points.
Using the points (-1, 2) and (3, 4):
m = (4 - 2) / (3 - (-1))
m = 2 / 4
m = 1/2
Step 2: Find the y-intercept (b) of the line.
To find the y-intercept, we can substitute the values of one of the given points into the slope-intercept form (y = mx + b) and solve for b.
Using the point (-1, 2):
2 = (1/2)(-1) + b
2 = -1/2 + b
b = 2 + 1/2
b = 5/2
Step 3: Write the equation of the line.
Using the slope-intercept form (y = mx + b), the equation of the line passing through the given points is:
y = (1/2)x + 5/2
Now, let's circle the two letters next to the correct equation. In this case, the correct equation is y = (1/2)x + 5/2, so we will circle the letters A and E.
Finally, let's write these letters in the two boxes at the bottom of the page that contain the number of this exercise.
Exercise Number: _______
Box 1: A
Box 2: E