Question

Write an equation in standard form that passes through (-5,5) and (3,20). Make sure there are no fractions in your answer.

Answer 1

The equation of line in standard form is:

$-15x+8y=115$

Further explanation:

Given points are:

(-5,5) and (3,20)

Let (x1,y1) = (-5,5)

Let (x2,y2) = (3,20)

The general equation is:

y=mx+b

We have to find the slope first

$m=\frac{y_2-y_1}{x_2-x_1}\\= \frac{20-5}{3+5}\\=\frac{15}{8}$

$y=\frac{15}{8}x+b$

To find the value of b, putting (3,20) in equation

$20=\frac{15}{8}(3)+b\\20=\frac{45}{8}+b\\20-\frac{45}{8}=b\\b=\frac{160-45}{8}\\b=\frac{115}{8}$

Putting the values of b and m in equation

$y=\frac{15}{8}x+\frac{115}{8}$

Multiplying both sides by 8

$8y=\frac{15}{8}x*8+\frac{115}{8}*8\\8y=15x+115\\-15x+8y=115$

Keywords: Standard form of equation of line, slope

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Answer 2

An equation in standard form that passes through (-5,5) and (3,20) is:

- 15x + 8y = 115

Further explanation

Solving linear equation mean calculating the unknown variable from the equation.

Let the linear equation : y = mx + c

If we draw the above equation on Cartesian Coordinates , it will be a straight line with :

m → gradient of the line

( 0 , c ) → y - intercept

Gradient of the line could also be calculated from two arbitrary points on line ( x₁ , y₁ ) and ( x₂ , y₂ ) with the formula :

$\large {\boxed{m = \frac{y_2 - y_1}{x_2 - x_1}}}$

If point ( x₁ , y₁ ) is on the line with gradient m , the equation of the line will be :

$\large {\boxed{y - y_1 = m ( x - x_1 )}}$

Let us tackle the problem.

This probem is about Linear Equation.

Let:

( -5 , 5 ) → ( x₁ , y₁ )

( 3, 20 ) → ( x₂ , y₂ )

We will use the formula as follows:

$y - y_1 = \frac{y_2 - y_1}{x_2 - x _1} \times ( x - x_1 )$

$y - 5 = \frac{20 - 5}{3 - (-5)} \times ( x - (-5) )$

$y - 5 = \frac{15}{8} \times ( x + 5 )$

$8( y - 5 ) = 15 ( x + 5 )$

$8y - 40 = 15x + 75$

$8y - 15x = 40 + 75$

$8y - 15x = 115$

$\texttt{ }$

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Answer details

Grade: High School

Subject: Mathematics

Chapter: Linear Equations

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point