Question

Find an equation for the line that passes through the points (-4,5) and (6,1)

Answer 1

To find the equation of the line passing through two points, you can use the slope-intercept form of the equation which is y = mx + b, where m is the slope and b is the y-intercept.

First, find the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

Given the points (-4,5) and (6,1), substitute the values into the formula:

m = (1 - 5) / (6 - (-4))
m = -4 / 10
m = -2/5

Now that we have the slope, we can substitute it into the equation y = mx + b, and select one of the points (let's choose (-4,5)) to solve for b:

5 = (-2/5)(-4) + b
5 = 8/5 + b

To get rid of the fraction, multiply everything by 5:

25 = 8 + 5b

Subtract 8 from both sides:

17 = 5b

Divide both sides by 5:

17/5 = b

Therefore, the value of b is 17/5.

Now we have the slope m = -2/5 and the y-intercept b = 17/5, so the equation of the line is:

y = (-2/5)x + 17/5