Question

Write an equation in slope-intercept form that goes through the points (5, 2) and (-3, -3).​
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Answer 1

Answer:-

Given points are (5 , 2) , ( - 3 , - 3).

We know that,

Equation of a line in slope intercept form is :

y - y₁ = m(x - x₁)

where m is slope of the line and (x₁ , y₁) is the first point.

Slope of a line (m) = (y₂ - y₁) / (x₂ - x₁)

Let ,

• y₂ = - 3
• y₁ = 2
• x₂ = - 3
• x₁ = 5

So,

⟹ m = ( - 3 - 2) / (- 3 - 5)

⟹ m = - 5 / - 8

⟹ m = 5/8

Now,

Required equation of the line is :

⟹ y - 2 = (5/8) (x - ( - 3))

⟹ (y - 2) × 8 = 5 (x + 3)

⟹ 8y - 16 = 5x + 15

⟹ 8y - 5x - 16 - 15 = 0

⟹ 8y - 5x - 31 = 0

∴ The required equation of the line is 8y - 5x - 31 = 0.