Question

Write an equation in standard form of the line that passes through

(–9, 4) and has a slope of –2/3.

(Add explanation please )

Also, Write the standard form of the equation y + 4 = – ⅗ (x – 8).

Answer 1

• 2x + 3y = - 6
• 3x + 5y = 4

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Standard form of a line

• ax + by = c

Given

• Point on the line (-9, 4) and a slope m = - 2/3

Use point- slope form and convert to standard

• y - y₁ = m(x - x₁), where (x₁, y₁) is the point on the line
• y - 4 = - 2/3(x - (-9))
• y - 4 = - 2/3(x + 9)
• 3(y - 4) = - 2(x + 9)
• 3y - 12 = - 2x - 18
• 2x + 3y = 12 - 18
• 2x + 3y = - 6

Standard of the line y + 4 = - 3/5(x - 8)

• y + 4 = - 3/5(x - 8)
• 5(y + 4) = - 3(x - 8)
• 5y + 20 = - 3x + 24
• 3x + 5y = 24 - 20
• 3x + 5y = 4