Question

A line passes through (2, −1) and (4, 5). which answer is the equation of the line?

a) −3x 5y=−13 negative 3 x plus 5 y equals negative 13
b) −3x 5y=13 negative 3 x plus 5 y equals 13 −3x
c) y =−7 negative 3 x plus y equals negative 7 −3x
d) y =17 negative 3 x plus y equals 17

Answer 1

The equation of the line passing through (2, -1) and (4, 5) is y = 3x - 7.

Step-by-step explanation:

To find the equation of the line that passes through the points (2, -1) and (4, 5), we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.

1. First, find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1). Substituting the values, we get m = (5 - (-1)) / (4 - 2) = 6 / 2 = 3.
2. Next, choose one of the given points (2, -1) and substitute the values of x, y, and m into the slope-intercept form. We get -1 = 3(2) + b. Solving for b, we find b = -7.
3. Finally, substitute the values of m and b into the equation y = mx + b. The equation of the line is therefore y = 3x - 7.