poveli1e

Answered

2022-01-31

68. Analyzing a Line A line is represented by the
equation $ax+by=4$ .

(a) When is the line parallel to the x-axis?

(a) When is the line parallel to the x-axis?

Answer & Explanation

tipoule137p

Expert

2022-02-01Added 10 answers

First, write the equation of line $ax+by=4$ in slope-intercept form, that is in the form of $y=mx+c$ ; here, m is the slope and c is the y-intercept of the line.

$ax+by=4$

$by=-ax+4$

$y=\frac{ax}{b}+\frac{4}{b}$

On comparing the above equation of line with standard slope-intercept form of line, the slope m is$-\frac{a}{b}$ .

The line is parallel of x-axis when the slope of the line is 0.

Apply the condition that the line is parallel of x-axis when the slope of the line is 0, that is$m=0$ . Here, $m=-\frac{a}{b}$ .

$m=0$

$-\frac{a}{b}=0$

$a=0$

Thus, the line$ax+by=4$ is parallel to x-axis when a=0.

On comparing the above equation of line with standard slope-intercept form of line, the slope m is

The line is parallel of x-axis when the slope of the line is 0.

Apply the condition that the line is parallel of x-axis when the slope of the line is 0, that is

Thus, the line

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