Question

Find the standard form of the equation of the line passing through the pair of points (1,6) and (-4,5).

a) 5x - y = -1
b) 6x - 5y = 1
c) x - 6y = -5
d) -x + 6y = 5

Answer 1

The standard form of the equation of a line passing through the points (1,6) and (-4,5) is x + 5y = 31.

Step-by-step explanation:

The standard form of the equation of a line is Ax + By = C, where A, B, and C are constants. To find the equation of the line passing through the points (1,6) and (-4,5), we can use the slope-intercept form (y = mx + b) and then convert it to the standard form.

1. Find the slope (m) using the formula m = (y2 - y1) / (x2 - x1). For the points (1,6) and (-4,5), the slope is (5 - 6) / (-4 - 1) = -1/5.
2. Using the slope-intercept form, y = mx + b, substitute the slope (-1/5) and one of the given points (1,6) to find the y-intercept, b. 6 = -1/5(1) + b. Solving for b, we get b = 31/5.
3. Substitute the slope (-1/5) and y-intercept (31/5) in the equation y = mx + b to get the equation in slope-intercept form: y = -1/5x + 31/5.
4. To convert the equation to standard form, multiply both sides by 5 to get 5y = -x + 31.
5. Rearrange the equation to have the x-term first: x + 5y = 31.

Therefore, the standard form of the equation of the line passing through the points (1,6) and (-4,5) is x + 5y = 31.