Question

linear equations color by number
perfect pumpkin surprise
circle the correct response to each question. use the answers to color to the picture. make sure your answers to each number match.
1a.) which of the following is a linear function?
yellow)
brown)
gray)
green)
2a.) which of the functions below is a linear function?
black) y = x - 7
yellow) y = |x| - 7
orange) y = x² - 7
brown) y = (1/x) - 7
3a.) what are the x - and y - intercepts of the line graphed?
pink) (4, 0) and (0, - 2)
orange) ( - 2, 0) and (0, 4)
blue) ( - 4, 0) and (0, 2)
green) (2, 0) and (0, - 4)
4a.) what is the x - intercept of 4x + 2y = 6?
blue) 1/3
green) 3/2
purple) 2/3
gray) 3
5a.) what is the slope of a vertical line?
purple) positive
black) negative
yellow) zero
pink) undefined
6a.) what is the slope of the line containing the ordered pair (2, 3) and ( - 4, 0)?
orange) - 2
blue) 1/2
pink) - 1/2
brown) 2
7a.) which equation describes the line with slope - 4 and y - intercept 2?
gray) y = - 4x + 2
black) y = 4x - 2
brown) y = - 4x - 2
blue) y = 4x + 2
8a.) what is the slope of the line graphed?
purple) - 3/2
black) 2/3
green) - 2/3
orange) 3/2

Explanation:

Step1: Recall linear - function definition

A linear function has a graph that is a straight line and can be written in the form $y = mx + b$. For 1A, the third graph (Gray) is a horizontal line which is a special case of a linear function ($y = c$, where $c$ is a constant). For 2A, $y=x - 7$ (Black) is in the form $y = mx + b$ with $m = 1$ and $b=-7$.

Step2: Find intercepts

For 3A, to find the $x$-intercept, set $y = 0$ and for the $y$-intercept, set $x = 0$. For the given line, when $y = 0$, $x = 4$ and when $x = 0$, $y=-2$ (Pink). For 4A, set $y = 0$ in $4x+2y = 6$, then $4x=6$, $x=\frac{3}{2}$ (Green).

Step3: Recall slope concepts

For 5A, the slope of a vertical line is undefined (Pink) since the change in $x$ is 0 and slope $m=\frac{\Delta y}{\Delta x}$. For 6A, use the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)=(2,3)$ and $(x_2,y_2)=(-4,0)$. So $m=\frac{0 - 3}{-4 - 2}=\frac{-3}{-6}=\frac{1}{2}$ (Blue).

Step4: Use slope - intercept form

For 7A, the slope - intercept form of a line is $y=mx + b$, with $m=-4$ and $b = 2$, so $y=-4x + 2$ (Gray). For 8A, using two points on the line, if we assume two points $(0,2)$ and $(3,0)$, then $m=\frac{0 - 2}{3-0}=-\frac{2}{3}$ (Green).

Answer:

1A. Gray
2A. Black
3A. Pink
4A. Green
5A. Pink
6A. Blue
7A. Gray
8A. Green