Question

Which of the following represents the equation of a line that passes through the points (2, -3) and (4, 5) in the standard (x, y) coordinate plane?

a. y = 2x + 5
b. y = 2x - 3
c. y = -2x + 5
d. y = -2x - 3

Answer 1

To find the equation of a line passing through two points, we use the slope-intercept form of a linear equation (y = mx + b). We find the slope (m) using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the given points. By substituting one point and the slope into the equation, we can solve for the y-intercept (b) and write the equation of the line.

Step-by-step explanation:

To find the equation of a line that passes through two given points, we can use the slope-intercept form of a linear equation, y = mx + b.

First, we need to find the slope (m) of the line. The slope is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two given points.

For the points (2, -3) and (4, 5), the slope is (5 - (-3)) / (4 - 2) = 8 / 2 = 4.

Next, we can substitute one of the points and the slope into the equation y = mx + b, and solve for b. Let's use the point (2, -3): -3 = 4(2) + b. Solving for b, we get b = -11.

Now that we have the slope (4) and the y-intercept (b = -11), we can write the equation of the line. The correct equation is y = 4x - 11.