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3 years ago

The points (–6, 0) and (–4, 2) fall on a particular line. What is its equation in slope-intercept form?

Mathematics

1 answer:

Elodia [21]3 years ago

5 0

Answer:

The answer to your question is y = x + 6

Step-by-step explanation:

Data

A (-6, 0)

B (-4, 2)

Process

1.- Calculate the slope of the line

x1 = -6 y1 = 0

x2 = -4 y2 = 2

Slope = (y2 - y1)/(x1 - x2)

Substitution

Slope = (2 - 0)/(-4 + 6)

Simplification

Slope = 2/2

Slope = m = 1

2.- Find the equation of the line

Formula

y - y1 = m(x - x1)

Substitution

y - 0 = 1(x + 6)

Simplification

y = x + 6

Result

y = x + 6

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$\huge\underline{\frak{ \: \: \: \: \: \: Solution : \: \: \: \: \: \: }} \\ \\$

$\frak {\pink{Let}}\begin{cases} \sf{\red{Breadth \: be \: x}}\\ \sf{\orange{The \: Length = x + 9}}\end{cases} \\$

$\bigstar \: \underline{\textsf{According to the given Question :} }\\ \\$

$:\implies \sf Area = Length \times Breadth \\ \\ \\$

$:\implies \sf 360=(x + 9 ) x \\ \\ \\$

$:\implies \sf 360= {x}^{2} + 9x \\ \\ \\$

$:\implies \sf {x}^{2} + 9x - 360 = 0\\ \\ \\$

$:\implies \sf {x}^{2} + 24x - 15x - 360 = 0\\ \\ \\$

$:\implies \sf x(x + 24) - 15(x + 24) = 0\\ \\ \\$

$:\implies \sf (x + 24) \: (x - 15) = 0\\ \\ \\$

$:\implies \underline{ \boxed{ \sf x = - 24 \: or \: x = 15}}\\ \\ \\$

$\therefore\:\underline{\textsf{Ignoring the negative value, the Breadth of rectangular garden is \textbf{15 ft}}}. \\ \\ \\$

$\bigstar \: \underline{\textsf{Dimensions of rectangular garden :}} \\ \\$

$\bullet\:\:\textsf{The Breadth of rectangular garden = x = \textbf{15 ft.}} \\ \\$

$\bullet\:\:\textsf{The Length of rectangular garden = x + 9 = 15 + 9 = \textbf{24 ft.}} \\ \\$

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