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

Answer 1

To find the equation of the line that passes through the given points, we can use the point-slope form of a linear equation.

1. First, let's find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1).

Using the coordinates (-5, -1) and (5, -3):
m = (-3 - (-1)) / (5 - (-5))
= (-3 + 1) / (5 + 5)
= -2 / 10
= -1/5.

2. Now, let's use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept. We can use one of the given points (5, -3) to find the value of b.

Plugging in the values into the equation:
-3 = (-1/5)(5) + b
-3 = -1 + b
-3 + 1 = b
-2 = b.

3. We have our slope (m = -1/5) and y-intercept (b = -2), so the equation of the line is:
y = (-1/5)x - 2.

To practice this equation using Desmos, you can follow these steps:
1. Open the Desmos website on your browser.
2. In the toolbar, you will find a "+ New Expression" button. Click on it.
3. In the input box that appears, type the equation y = (-1/5)x - 2.
4. Press enter or click the "+" button next to the input box.
5. The graph will show the line passing through the given points (-5, -1) and (5, -3).