Question

For the linear equation 3x + 7y = 42: a. Determine the slope: b. Determine y- intercept if it exists: c. Express equation in slope-intercept form:

Answer 1

Answer: The required answers are

(a) the slope of the given line is
`-(3)/(7).`

(b) y-intercept exists and is equal to 6.

(c) the slope-intercept form of the line is
`y=-(3)/(7)x+6.`

Explanation: We are given the following linear equation in two variables :

`3x+7y=42~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

We are to :

(a) determine the slope,

(b) determine the y-intercept, if exists

and

(c) express equation in slope-intercept form.

We know that

The SLOPE_INTERCEPT form of the equation of a straight line is given by

`y=mx+c,` where m is the slope and c is the y-intercept of the line.

From equation (i), we have

`3x+7y=42\\\\\Rightarrow 7y=-3x+42\\\\\Rightarrow y=(-3x+42)/(7)\\\\\\\Rightarrow y=-(3)/(7)x+6.`

Comparing with the slope-intercept form, we get

`\textup{slope, m}=-(3)/(7),\\\\\\\textup{y-intercept, c}=6.`

Thus,

(a) the slope of the given line is
`-(3)/(7).`

(b) y-intercept exists and is equal to 6.

(c) the slope-intercept form of the line is
`y=-(3)/(7)x+6.`