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

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 [tex]y-y_{1}=m(x-x_{1})[/tex] , where m is the slope of the line and [tex](x_{1},y_{1})[/tex] 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 [tex]\frac{3}{5}[/tex]

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

standard form

∵ [tex]x_{1}[/tex] = 2 and [tex]y_{1}[/tex] = -4

∵ m = [tex]\frac{3}{5}[/tex]

- Substitute these values in the form of the equation below

∵ [tex]y-y_{1}=m(x-x_{1})[/tex]

∴ [tex]y-(-4)=\frac{3}{5}(x - 2)[/tex]

∴ [tex]y+4=\frac{3}{5}(x - 2)[/tex]

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

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