Answer:
Part 1) \(7x-4y=42\)
Part 2) \(9x+5y=-45\)
Part 3) \(6x+7y=14\)
part 4) \(5x+4y=20\)
Step-by-step explanation:
we know that
The standard form of the equation of the line is equal to
\(Ax + By = C\)
where
A is a positive integer
B, and C are integers
Part 1) Determine the standard form of the equation of the line that passes through \((6,0)\) and \((2,-7)\)
we know that
The formula to calculate the slope between two points is equal to
\(m=\frac{y2-y1}{x2-x1}\)
Substitute the values
\(m=\frac{-7-0}{2-6}\)
\(m=\frac{-7}{-4}\)
\(m=\frac{7}{4}\)
The equation of the line into point slope form is equal to
\(y-y1=m(x-x1)\)
we have
\(m=\frac{7}{4}\)
\(Point (6,0)\)
substitute
\(y-0=\frac{7}{4}(x-6)\)
\(y=\frac{7}{4}x-\frac{42}{4}\)
Multiply by \(4\) both sides
\(4y=7x-42\)
convert in standard form
\(7x-4y=42\)
Part 2) Determine the standard form of the equation of the line that passes through \((-5,0)\) and \((0,-9)\)
we know that
The formula to calculate the slope between two points is equal to
\(m=\frac{y2-y1}{x2-x1}\)
Substitute the values
\(m=\frac{-9-0}{0+5}\)
\(m=-\frac{9}{5}\)
The equation of the line into point slope form is equal to
\(y-y1=m(x-x1)\)
we have
\(m=-\frac{9}{5}\)
\(Point (-5,0)\)
substitute
\(y-0=-\frac{9}{5}(x+5)\)
\(y=-\frac{9}{5}x-9\)
Multiply by \(5\) both sides
\(5y=-9x-45\)
convert in standard form
\(9x+5y=-45\)
Part 3) Determine the standard form of the equation of the line that passes through \((-7,8)\) and \((0,2)\)
we know that
The formula to calculate the slope between two points is equal to
\(m=\frac{y2-y1}{x2-x1}\)
Substitute the values
\(m=\frac{2-8}{0+7}\)
\(m=-\frac{6}{7}\)
The equation of the line into point slope form is equal to
\(y-y1=m(x-x1)\)
we have
\(m=-\frac{6}{7}\)
\(Point (0,2)\)
substitute
\(y-2=-\frac{6}{7}(x-0)\)
\(y=-\frac{6}{7}x+2\)
Multiply by \(7\) both sides
\(7y=-6x+14\)
convert in standard form
\(6x+7y=14\)
Part 4) Determine the standard form of the equation of the line that passes through \((0,5)\) and \((4,0)\)
we know that
The formula to calculate the slope between two points is equal to
\(m=\frac{y2-y1}{x2-x1}\)
Substitute the values
\(m=\frac{0-5}{4-0}\)
\(m=-\frac{5}{4}\)
The equation of the line into point slope form is equal to
\(y-y1=m(x-x1)\)
we have
\(m=-\frac{5}{4}\)
\(Point (0,5)\)
substitute
\(y-5=-\frac{5}{4}(x-0)\)
\(y=-\frac{5}{4}x+5\)
Multiply by \(4\) both sides
\(4y=-5x+20\)
convert in standard form
\(5x+4y=20\)
