How do i write an equation in standard form when given the point (7,-3) and y intercept 2

Question

I have to find the equation in standard form given (7-3) and y intercept 2

Answer 1

Slope intercept form of the line is y = mx+b

m is slope and b is y intercept.

Given y intercept is 2 and passes through (7,-3).

if the line have y intercept we need another point to find equation of the line.

we can assume the line also passes through the origin (0,0) there is no y intercept.

Say the points are (x1,y1) = (7,-3) and (0,0) = (x2,y2).

m = (0-(-3))/(0-7) =3/-7

Slope is -3/7.

 required line equation is y-y1 = m (x-x1)

y+3 = -3/7(x-7)

Multiple to each side by 7.

7(y+3) = 7(-3/7)(x-7)

7y+21 = -3x+21

Subtract 21 from each side.

7y+21-21 = -3x+21-21

7y = -3x

y = -3x/7.

Line equation is y = -3x/7.

Answer 2

The line passes through (7,-3) and y intercept 2

So the line crosses y  axis at (0, 2).

Slope - intercept - form of a line equation is y = mx + c, where, m is slope and c is y - intercept.

Substitute the values of m = -5/7 c = 2 in slope - intercept - form of a line equation : y = mx + c.

Standard form of line equation ax + by = c

Required line equation is .

 

Answer 3

The standard form line equation is Ax + By = C. A shouldn't be negative, A and B shouldn't both be zero, and A, B and C should be integers.

The point is (7, - 3) and y - intercept is 2.

The slope - intercept form of line equation is y = mx + b, where m is slope and b is the y - intercept.

The line equation is y = mx + 2.

To find the slope m, substitute the value of (x, y) = (7, - 3) in the above equation.

(- 3) = m(7) + 2

- 5 = 7m

- 5/7 = m.

The slope - intercept form of line equation is y = (- 5/7)x + 2.

Write the equation y = (- 5/7)x + 2 in standard form of line equation.

Multiply each side by 7.

7y = - 5x + 14

Add 5x to  each side.

7y + 5x = 14.

To check the obtained equation, substitute the value of (x, y) = (7, - 3) in the obtained equation.

5(7) + 7(- 3) = 14

35 - 21 = 14

14 = 14.

The above statement is true, so the obtained equation is correct.

The standard form of line equation is 5x + 7y = 14.