Asystem of linear equations includes the line tha is created by the equation y=x+3,graphed below, and the line through the points (3,1)and(4.3)

Step-by-step explanation:

(3,1) , (4,3)

slope = (y2 - y1) / (x2 - x1)

slope = (3 - 1) / (4 - 3) = 2/1 = 2

y = mx + b

slope(m) = 2

u can use either of ur points(3,1)...x = 3 and y = 1

now we sub and find b, the y int

1 = 2(3) + b

1 = 6 + b

1 - 6 = b

-5 = b

ur other equation is : y = 2x - 5

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

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 ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form