Answer:
Step-by-step explanation: The formula for the line that intersects at (8,-5) and is parallel to line x+y = 8 is given by the algebraic expression y = -x +3.
What is Algebraic expression?
The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values.
Variables and constants can both be used in an algebraic expression.
A coefficient is any quantity that is added before a variable and then multiplied by it.
The Algebraic expression in this case is:
x + y = 8
which traverses points (8,-5)
Let's start by utilizing the point-intercept equation of line, which is provided by: to determine the slope of line m, that is parallel towards the line x + y = 8.
y = mx + c →(1)
x + y = 8
y = -x + 8
Comparing the aforementioned Algebraic expression to equation (1), we obtain
m = -1
The slope of the line parallel to the line x + y = 8 will now be the same, and it will be m = -1.
Let's use the point-slope equations of line to determine the linear equation now:
(y-y₁) = m(x-x₁)
Changing every value in the equation above to obtain the Algebraic expression for a line
(y-(-5)) = -1(x-8) (x-8)
(y+5) = -x+8
y + 5 = -x +8
y = -x +3
The formula for the line that intersects at (8,-5) and is parallel to line x+y = 8 is given by the algebraic expression y = -x +3