D
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (3, 0 ) and (x₂, y₂ ) = (0, - 5 )
m = [tex]\frac{-5-0}{0-3}[/tex] = [tex]\frac{5}{3}[/tex]
line crosses y-axis at (0, - 5 ) hence c = - 5
y = [tex]\frac{5}{3}[/tex] x - 5 ← in slope-intercept form
the equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
rearrange slope-intercept form into standard form
multiply all terms by 3
3y = 5x - 15 ( subtract 3y and add 15 to both sides )
5x - 3y = 15 ← in standard form → D
