Answer:
Here's what I get
Step-by-step explanation:
1. Interpreting graphs
a. Identifying slope and intercept
Line A
The line passes through the points (0, 4) and (3, 0).
[tex]\text{Slope} = \dfrac{y_{2} -y_{1}}{ x_{2} -x_{1}} = \dfrac{0 - 4 }{3 - 0} = -\dfrac{4}{3}[/tex]
y-intercept = (0, 4)
x-intercept = (3, 0)
Line B
The line passes through the points (-2, 0) and (0, 2).
[tex]\text{Slope} = \dfrac{2 - 0}{0 - (-2)} = -\dfrac{2}{0 + 2}= \dfrac{2}{2} = 1[/tex]
y-intercept = (0, 2)
x-intercept = (-2, 0)
Line C
The line passes through the points (0, -4) and (2, 0)
[tex]\text{Slope} = \dfrac{0 - (-4) }{2 - 0} = \dfrac{0 + 4}{2}= \dfrac{4}{2} = 2[/tex]
y-intercept = (0, -4)
x-intercept = (2, 0)
[tex]\begin{array}{cccc}\textbf{Line}& \textbf{Rate}& \textbf{y-intercept} & \textbf{x-intercept}\\\textbf{A} & -\frac{4}{3} & (0,4) & (3, 0)\\\textbf{B} & 2 & (0, 2) & (-4, 0)\\\textbf{C} & 1 & (0, -4) & (2, 0)\\\end{array}[/tex]
b. Matching graphs to equations
The graphs all have different slopes: -⁴/₃, 1, and 2.
The graph with the negative slope is Line A.
The graph with the steepest positive slope is Line C.
The graph with a less steep slope is Line B. So,
y = 3 - x ⟶ Line A
y = 2+ x ⟶ Line B
y = -4 + 2x ⟶ Line C
2. Finding Slope, intercepts, and equations
a.
[tex]\text{Slope} = \dfrac{y_{2} -y_{1}}{ x_{2} -x_{1}} = \dfrac{6 - 3}{6 - 0} = \dfrac{3}{6} =\dfrac{1}{2}[/tex]
y-intercept = (0, 3)
y = 3 + ½x
b.
[tex]\text{Slope} = \dfrac{6 - 18}{6 - 2} = -\dfrac{12}{4} = -3[/tex]
That means, if we increase x by two units, we decrease y by six units.
If we start at (2, 18) and decrease x by two units, we increase y by six units. Then, y = 24;
y-intercept = (0, 24)
y = 24 - 3x
c.
[tex]\text{Slope} = \dfrac{9 - 9}{8 - 2} = \dfrac{0}{6} = 0[/tex]
That means, whatever we do to x, the value of y does not change.
y-intercept = (0, 9)
y = 9 + 0x
The equation is
y = 9
