Answers:
Slope of line SP: -1
Slope of line FJ: -1
Point-Slope Form of Line FJ: [tex]y=-x-6[/tex]
What to type inside the orange box? You must type "-x-6".
Step-by-step explanation:
Concept. A parallel line to line SP. A parallel line is a line that has the same slope as another line, therefore, the line parallel to SP has the same slope of SP.
Let's solve!
1. Find the slope of line SP.
Line SP's expression is: [tex]y=-x-14[/tex].
The slope of a linear function is always given by the coefficient of x when the equation is solved for y. Hence, the slope of line SP is -1, because x is being multiplied by -1.
2. Form the equation for line FJ.
Use the formula for finding linear equations: [tex]y-y_{1} =m(x-x_{1} )[/tex], where m is the slope of the line, [tex]x_{1}[/tex] is the x value of a point where the line passes, and [tex]y_{1}[/tex] is the y value of a point where the line passes. [tex]x_1[/tex] and [tex]y_1[/tex] must be taken from a single point where the function passes.
Let's take the formula and find the equation for line FJ:
a. Substitute in the formula.
[tex]y-(0) =(-1)(x-(-6) )[/tex]
b. Simplify.
[tex]y-(0) =(-1)(x-(-6) )\\ \\y=(-1)(x+6)\\ \\y=-x-6[/tex]
3. Express your answers.
Slope of line SP: -1
Slope of line FJ: -1
Point-Slope Form of Line FJ: [tex]y=-x-6[/tex]
