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

Vectors and spaces
ANSWERED Write an equation of the line that passes through (3, 1) and (0, 10) 2021-03-02

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 $$(x_{1}, y_{1})$$ and (0,10) is $$(x_{2}, y_{2})$$. Using two points, we can use find the slope with the following formula.
$$\displaystyle{\frac{{{\left({y}{2}-{y}{1}\right)}}}{{{\left({x}{2}-{x}{1}\right)}}}}$$
Replace these variables with the values.
$$\displaystyle{\frac{{{\left({10}-{1}\right)}}}{{{\left({0}-{3}\right)}}}}=-{3}$$
-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).
$$10 = -3(0) + b$$
$$b = 10$$
(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:
$$y = -3x + 10$$