Question

Indicate the equation of the line, in standard form, that passes through (2, -4) and has a slope of 3/5.

Answer 1

The equation of the line in standard form is 3x - 5y = 26

Step-by-step explanation:

Let us revise the forms of the linear equation

• The slope intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept
• The point-slope form is $y-y_{1}=m(x-x_{1})$ , where m is the slope of the line and $(x_{1},y_{1})$ is a point on the line
• The standard form is Ax + By = C, where A, B, and C are constant
• The general form is Ax + By + C = 0, where A, B, and C are integers

∵ The line passes through point (2 , -4)

∵ The slope of the line is $\frac{3}{5}$

- Let us using the point-slope form and then change it to the

  standard form

∵ $x_{1}$ = 2 and $y_{1}$ = -4

∵ m = $\frac{3}{5}$

- Substitute these values in the form of the equation below

∵ $y-y_{1}=m(x-x_{1})$

∴ $y-(-4)=\frac{3}{5}(x - 2)$

∴ $y+4=\frac{3}{5}(x - 2)$

Let us change it to standard form

- Multiply each side my 5 to cancel the denominator in the

   right hand side

∴ 5(y) + 5(4) = 3(x - 2)

- Simplify the two sides

∴ 5y + 20 = 3x - 6

- Add 6 to both sides

∴ 5y + 26 = 3x

- Subtract 5y from both sides

∴ 26 = 3x - 5y

- Switch the two sides

∴ 3x - 5y = 26

The equation of the line in standard form is 3x - 5y = 26

Learn more:

You can learn more about the linear function in brainly.com/question/12363217

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