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Vadim26 [7]
3 years ago
8

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

pe-intercept form:
Mathematics
1 answer:
algol133 years ago
3 0

Answer:  The required answers are

(a) the slope of the given line is -\dfrac{3}{7}.

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

(c) the slope-intercept form of the line is y=-\dfrac{3}{7}x+6.

Step-by-step 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=\dfrac{-3x+42}{7}\\\\\\\Rightarrow y=-\dfrac{3}{7}x+6.

Comparing with the slope-intercept form, we get

\textup{slope, m}=-\dfrac{3}{7},\\\\\\\textup{y-intercept, c}=6.

Thus,

(a) the slope of the given line is -\dfrac{3}{7}.

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

(c) the slope-intercept form of the line is y=-\dfrac{3}{7}x+6.

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To find the slope, we need to use the slope formula which is as follows: m = (y2 - y1) / (x2 - x1). We will plug in each x and y coordinate from our points above, respectively.

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Step-by-step explanation:

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