Question

Write an equation of the line passing through (-1,4) and (6,5). Give the answer in Standard form

Answer 1

To find the equation of the line through (-1, 4) and (6, 5), calculate the slope (m), which is 1/7, then use the point-slope form with one point, and convert to standard form to obtain the equation x - 7y = -29.

Step-by-step explanation:

To write the equation of the line passing through the points (-1, 4) and (6, 5) in standard form, we need to follow these steps:

1. Find the slope (m) of the line using the formula m = (y2 - y1) / (x2 - x1).
2. Use the point-slope form of the linear equation, y - y1 = m(x - x1), to write the equation.
3. Convert the equation to standard form, Ax + By = C, where A, B, and C are integers.

First, calculate the slope:

m = (5 - 4) / (6 - (-1)) = 1 / 7

Next, using the point (-1,4) and the point-slope form:

y - 4 = (1/7)(x - (-1))

Multiply through by 7 to clear the fraction:

7y - 28 = x + 1

Rearrange to standard form:

-x + 7y = 29

To get the coefficients in standard form to be integers, we can multiply through by -1:

x - 7y = -29