Question

1. (l107) select the shape of the graph of this two - variable equation: $y = 2x+3$ a) two - humped curve b) line c) parabola d) circle e) square 5. (l107) select the shape of the graph of this two - variable equation: $y=-2x^{2}$ a) parabola b) two - humped curve c) circle d) square e) line

Explanation:

Step1: Recall linear - equation form

The general form of a linear equation is $y = mx + b$, where $m$ and $b$ are constants. The equation $y = 2x+3$ is in this form with $m = 2$ and $b = 3$. The graph of a linear equation is a line.

Step2: Recall quadratic - equation form

The general form of a quadratic equation is $y=ax^{2}+bx + c$. The equation $y=-2x^{2}$ is a quadratic equation with $a=-2$, $b = 0$ and $c = 0$. The graph of a quadratic equation is a parabola.

Answer:

1. b) line
2. a) parabola