Question

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

Vectors and spaces
ANSWERED
asked 2021-03-01
Write an equation of the line that passes through (3, 1) and (0, 10)

Answers (1)

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:
\(y = -3x + 10\)

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