Answer:
Step-by-step explanation:
1 Line A: The Constant rate is the Slope
Slope = It is going down so it is a negative slope
Slope formula = Rise/Run OR y/x
Slope = -1/1 = -1
Y-intercept = Starting point = 3
X-intercept = Where y is 0 = So the x-intercept is 3
Line B: The Constant rate is the Slope
Slope = It is going up so it is a positive slope
Slope formula = Rise/Run OR y/x
Slope = 1/1 = 1
Y-intercept = Starting point = 2
X-intercept = Where y is 0 = So the x-intercept is -2
Line C: The Constant rate is the Slope
Slope = It is going up so it is a positive slope
Slope formula = Rise/Run OR y/x
Slope = 2/1 = 2
Y-intercept = -4
X-intercept = Where y is 0 = So the x-intercept is 2
b. Line A: y = -x + 3 OR y = 3 - x
Line B: y = x + 2 OR y = 2 + x
Line C: y = 2x - 4 OR y = -4 + 2x
2a. It is a positive slope because the line is going up.
Slope = Rise/Run = 3/6 = 1/2
Y-intercept = Starting point = 3
Equation: y = 1/2x + 3
b. It is a negative slope because the line is going down.
Slope = Rise/Run = -6/2 = -3
Y-intercept = Starting point = Unknown, So we have to find it.
The formula is; [tex]y-y_{1} = m(x-x_{1})[/tex]
Just pick a point and substitute. I am going to use the point (2, 18).
y - 18 = -3(x - 2)
Distribute first; y - 18 = -3x + 6
Add 18 to both sides
y = -3x + 24; This is the equation of the line.
The y-intercept is 24.
The slope is -3
c. It is a horizontal line so the slope is 0. The slope of any horizontal line is 0.
We can still try to solve for the slope.
Slope = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] = [tex]\frac{9-9}{8-2}[/tex] = [tex]\frac{0}{6}[/tex] = 0
So the slope is still 0
Y-intercept = Starting point = 9
The line keeps going straight on point 9.
We can still calculate though!
[tex]y-y_{1}=m(x-x_{1} )[/tex]
So I will pick a point; (2, 9)
y - 9 = 0(x - 2)
Distribute though; y - 9 = 0 - 0
Add 9 to both sides
y = 9
The y-intercept is 9
Equation of a line: y = 9 since there is no slope.
