Question

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

How to put this on desmos practice mode to find the equation?

Answer 1

To find the equation of the line that passes through the points (-5, -1) and (5, -3), you can use the point-slope formula, which states that a line passing through the point (x₁, y₁) with slope m has an equation of the form:

y - y₁ = m(x - x₁)

First, calculate the slope (m) using the coordinates of the two points:

m = (y₂ - y₁) / (x₂ - x₁)

Substituting the values (-5, -1) and (5, -3) into the formula:

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

Now, choose any of the given points (let's choose (-5, -1)) and substitute the values of x₁, y₁, and m into the equation:

y - y₁ = m(x - x₁)
y - (-1) = (-1/5)(x - (-5))
y + 1 = (-1/5)(x + 5)

This is the equation of the line that passes through the given points.

Regarding the second part of your question, Desmos Practice Mode cannot be used to find the equation directly. However, you can use the Desmos graphing calculator to verify the equation by entering it into the calculator and observing the line passing through the given points.