Question

What is an equation of the line that passes through the points left bracket, minus, 5, comma, 1, right bracket
(
−
5
,
1
)
(−5,1) and left bracket, 5, comma, minus, 3, right bracket
(
5
,
−
3
)
(5,−3)?

Answer 1

To find the equation of the line that passes through the given points, we first need to find the slope of the line using the formula:

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

Using the points (-5, 1) and (5, -3), we can substitute the values into the formula:

m = (-3 - 1) / (5 - (-5))
m = (-4) / 10
m = -2/5

Now that we have the slope, we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

Using the first point (-5, 1), we can substitute the values into the equation:

y - 1 = (-2/5)(x - (-5))
y - 1 = (-2/5)(x + 5)
y - 1 = (-2/5)x - 2
y = (-2/5)x - 1

So, the equation of the line that passes through the points (-5, 1) and (5, -3) is y = (-2/5)x - 1.