 coexpennan

2021-03-01

Write an equation of the line that passes through (3, 1) and (0, 10) averes8

When we are given two points and we have to write the equation that passes through the two points, we can first find the slope. Let's say (3,1) is $\left({x}_{1},{y}_{1}\right)$ and (0,10) is $\left({x}_{2},{y}_{2}\right)$. Using two points, we can use find the slope with the following formula.
$\frac{\left(y2-y1\right)}{\left(x2-x1\right)}$
Replace these variables with the values.
$\frac{\left(10-1\right)}{\left(0-3\right)}=-3$
-3 is the slope. Next, we have to find the y-intercept. We can plug in the values that we know using the following formula:
$y=mx+b$
$y=-3x+b$
Now we can choose one of the points, and plug in the values in the equation above. Let's use (0,10).
$10=-3\left(0\right)+b$
$b=10$
(Note: The point (0,10) is already on the y-axis, meaning that 10 is the y-intercept. We didn't need to do the step above for this specific problem.)
So the complete equation of the line that passes through the two points is:
$y=-3x+10$ karton

Step 1: Find the slope ($m$)
The slope of a line passing through two points $\left({x}_{1},{y}_{1}\right)$ and $\left({x}_{2},{y}_{2}\right)$ can be calculated using the formula:
$m=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}$
Substituting the given points, we have:
$m=\frac{10-1}{0-3}=\frac{9}{-3}=-3$
Step 2: Use the point-slope form
Now that we have the slope ($m=-3$) and one of the points $\left({x}_{1},{y}_{1}\right)=\left(3,1\right)$, we can substitute these values into the point-slope form to get the equation of the line:
$y-1=-3\left(x-3\right)$
Step 3: Simplify the equation
Distribute the $-3$ on the right side:
$y-1=-3x+9$
Step 4: Move all terms to one side
To get the equation in standard form, we need to move all the terms to one side of the equation:
$3x+y=10$
This is the final equation of the line passing through the points (3, 1) and (0, 10). star233

The equation of the line passing through $\left(3,1\right)$ and $\left(0,10\right)$ is:
$y-1=\frac{10-1}{0-3}\left(x-3\right)$ alenahelenash

$y=-3x+10$
Explanation:
$y-{y}_{1}=m\left(x-{x}_{1}\right)$ where $\left({x}_{1},{y}_{1}\right)$ is a point on the line, and $m$ is the slope of the line.
Given the points $\left(3,1\right)$ and $\left(0,10\right)$, we can calculate the slope using the formula:
$m=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}$
Substituting the coordinates of the given points:
$m=\frac{10-1}{0-3}$
Simplifying the expression:
$m=\frac{9}{-3}$
$m=-3$
Now, we can choose either of the given points and substitute the values into the point-slope form equation. Let's use the point $\left(3,1\right)$. Substituting the values of ${x}_{1}$, ${y}_{1}$, and $m$:
$y-1=-3\left(x-3\right)$
Simplifying the equation:
$y-1=-3x+9$
Adding $1$ to both sides:
$y=-3x+10$
Therefore, the equation of the line that passes through the points $\left(3,1\right)$ and $\left(0,10\right)$ is:
$y=-3x+10$

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