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Write an equation of the line that passes through the points (2,-4) (1,6)

User Noumenal
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Answer: y - 6 = -10 (x - 1) OR y = - 10 x + 16

Explanation:

For us to write the equation for this line, we need to (1) find the slope of the line, and (2) use one of the points to write an equation:

The question gives us two points, (2,-4) & (1,6), from which we can find the slope and later the equation of the line.

Finding the Slope

The slope of the line (m) = (y₂ - y₁) ÷ (x₂ - x₁)

= (-4 - 6) ÷ (2 - 1)

= - 10 ÷ 1

= - 10

Finding the Equation

We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line; where (x₁ , y₁) = (1, 6):

⇒ y - 6 = -10 (x - 1)

we could also transform this into the slope-intercept form ( y = mx + c)

since y - 6 = -10 (x - 1)

y - 6 = -10 x - 10 (-1)

⇒ y = - 10x + 16

To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.

Write an equation of the line that passes through the points (2,-4) (1,6)-example-1
User Naganalf
by
8.1k points

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