Question

Develop the line equation having point (4,5 )and (1,2)

Answer 1

The equation of the line passing through the points (4,5) and (1,2) is found by calculating the slope and then expressing the equation in slope-intercept form, resulting in y = x + 1.

Step-by-step explanation:

To develop the line equation for the points (4,5) and (1,2), we follow these steps:

1. Calculate the slope (m) using the formula m = (Y2 - Y1) / (X2 - X1), where (X1, Y1) and (X2, Y2) are the given points.
2. Use one of the points and the slope to write the equation in point-slope form, which is y - y1 = m(x - x1).
3. Rearrange the equation to slope-intercept form, y = mx + b, where b is the y-intercept.

Now, let's calculate:

1. Slope calculation: m = (5 - 2) / (4 - 1) = 3 / 3 = 1
2. Point-slope form: Using point (4,5), the equation is y - 5 = 1(x - 4)
3. Slope-intercept form: Simplifying the above equation gives us y = x + 1

The equation of the line is y = x + 1.