Question8 Which of the following equations represents a line without a $y$ -intercept? (a) $y=4$ (b) $x=-4$ (c) $x+y=2$ (d) $y=3 x$

Studdy Solution

STEP 1

1. A line without a $y$ -intercept is a vertical line.
2. A vertical line is represented by an equation of the form $x = c$ , where $c$ is a constant.
3. We are given four equations and need to determine which one represents a vertical line.

STEP 2

1. Identify the form of each equation.
2. Determine which equation represents a vertical line.

STEP 3

Identify the form of each equation.
- (a) $y = 4$ is a horizontal line with a $y$ -intercept at $(0, 4)$ . - (b) $x = -4$ is a vertical line with no $y$ -intercept. - (c) $x + y = 2$ can be rearranged to $y = -x + 2$ , which is a line with a $y$ -intercept at $(0, 2)$ . - (d) $y = 3x$ is a line with a $y$ -intercept at $(0, 0)$ .

STEP 4

Determine which equation represents a vertical line.
From STEP_1, we identified that equation (b) $x = -4$ is a vertical line.
The equation that represents a line without a $y$ -intercept is:
$\boxed{x = -4}$

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