Question

A line passes through (−1, 7) and (2, 10).

Which answer is the equation of the line?



Responses

−3x+y=16
negative 3 x plus y equals 16

−x+y=8
negative x plus y equals 8

−x+y=12
negative x plus y equals 12

−3x+y=4
negative 3 x plus y equals 4

Answer 1

To find the equation of the line passing through the points (-1, 7) and (2, 10), we can use the point-slope form of a line, which is given by:

y - y₁ = m(x - x₁)

where (x₁, y₁) is a point on the line, and m is the slope of the line.

First, let's find the slope (m) using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Using the points (-1, 7) and (2, 10), we have:

m = (10 - 7) / (2 - (-1))
= 3 / 3
= 1

Now that we have the slope, we can choose one of the points to substitute into the point-slope form. Let's use (-1, 7) as (x₁, y₁):

y - 7 = 1(x - (-1))
y - 7 = x + 1
y = x + 1 + 7
y = x + 8

Therefore, the equation of the line passing through the points (-1, 7) and (2, 10) is:

y = x + 8

None of the given options match the correct equation.