Final answer:
The equation of the line passing through the points (3, 7) and (-1, -1) is found using the slope formula and point-slope form, resulting in the line equation y = 2x + 1.
Step-by-step explanation:
To write the equation of the line that passes through the points (3, 7) and (-1, -1), we first need to find the slope of the line (m) using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points. Substituting the given points into the formula:
m = (-1 - 7) / (-1 - 3)
= -8 / -4
= 2
Now, using the slope and one of the points, we apply the point-slope form of the line equation y - y1 = m(x - x1). Let's use the point (3, 7):
y - 7 = 2(x - 3)
To put the equation in slope-intercept form (y = mx + b), we simplify:
y - 7 = 2x - 6
y = 2x + 1
Next, we can use one of the given points, e.g., (3, 7), and the slope m to find the y-intercept b. Using the equation y = mx + b and plugging in the values y = 7, x = 3, and m = -2, we can solve for b: 7 = -2 * 3 + b = -6 + b. Solving for b, we get b = 7 + 6 = 13.
Therefore, the equation of the line that passes through the points (3, 7) and (-1, -1) is y = 2x + 1.