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 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).
To find the equation of a line that passes through two given points, you can use the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope of the line and b represents the y-intercept.
1. First, find the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Let's plug in the coordinates of the given points:
x1 = -5, y1 = -1
x2 = 5, y2 = -3
m = (-3 - (-1)) / (5 - (-5))
m = (-3 + 1) / (5 + 5)
m = -2 / 10
m = -1/5
2. Now that we have the slope (m), we can use one of the given points and slope to find the y-intercept (b) by rearranging the slope-intercept form of the equation and solving for b:
y = mx + b
-1 = (-1/5)(-5) + b
Using the point (-5, -1):
-1 = (1) + b
-1 - 1 = b
b = -2
3. Now we have the slope (m = -1/5) and the y-intercept (b = -2). So the equation of the line passing through the points (-5,-1) and (5,-3) is:
y = (-1/5)x - 2
To put this equation on Desmos practice mode, you can go to the Desmos website (www.desmos.com) and graph the equation by typing it directly into the calculator input box or using the equation editor.
To find the equation of the line that passes through the given points, we can use the point-slope form of the equation of a line.
1. Start by determining the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Let's plug in the coordinates of the points into the formula:
m = (-3 - (-1)) / (5 - (-5))
= (-3 + 1) / (5 + 5)
= -2 / 10
= -1/5
So, the slope of the line passing through the points (-5, -1) and (5, -3) is -1/5.
2. Once we have the slope, we can choose one of the points (let's use (-5, -1)) and substitute the values into the point-slope form equation:
y - y1 = m(x - x1)
Substituting the values, we get:
y - (-1) = (-1/5)(x - (-5))
y + 1 = (-1/5)(x + 5)
3. Distribute the -1/5 on the right side of the equation:
y + 1 = (-1/5)x - 1
4. Simplify the equation:
y = (-1/5)x - 2
Therefore, the equation of the line passing through the points (-5, -1) and (5, -3) is y = (-1/5)x - 2.
To put this on Desmos practice mode, you can simply enter the equation "y = (-1/5)x - 2" into the input area on the Desmos website or application. Desmos will graph the line for you, allowing you to explore it and practice manipulating equations and points.