If an item

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

algol13

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 $y=-\dfrac{3}{7}x+6.$

3 0

3 years ago

Evaluate each expression if a=4, b=6 and c=3 5b-6c

iragen [17]

Answer:

it is 12

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Quadrilateral ABCD is dilated by a scale factor of 2 centered around (2, 2). Which statement is true about the dilation?

arsen [322]

Answer:

Option (B) is true i.e segment B'D' will run through (2,2) and will be longer than the segment BD.

Step-by-step explanation:

As the assumption quadrilateral ABCD is shown in figure a.

First located the center of the dilation which is located at (2,2) as shown in figure b.

The next thing we want to do is to determine the distance of the center of dilation to each of the points of quadrilateral ABCD as shown in figure b.

Let’s just start with the distance from the center to the point A, but notice we don’t have to move up and down in y direction. So, what we have to do is to increase this by the factor 2. Because this horizontal distance is 1 i.e. the distance from dilation center (2,2) to point A, we just have to multiply by 2 which would be a distance of 2 and this point right here will be the new location of point A’ (0,2).

And the distance from the center to the point C is the horizontal distance of 2 i.e. the distance from dilation center (2,2) to point C, we just have to multiply by 2 which would be a distance of 4 and this point right here will be the new location of point C’ (6,2).

And the distance from the center to the point B is the upward vertical distance of 1 i.e. the distance from dilation center (2,2) to point B, we just have to multiply by 2 which would be a vertical distance of 2 and this point right here will be the location of point B’ (2,4).

And similarly the distance from the center to the point D is the downward vertical distance of 1 i.e. the distance from dilation center (2,2) to point D, we just have to multiply by 2 which would be a vertical distance of 2 and this point right here will be the location of point D’ (2,0).

So, Quadrilateral A'B'C'D' is dilated by a scale factor of 2 centered around (2, 2).

Just notice in figure b that the segment B'D' will run through (2,2) and will be longer than the segment BD.

So,option (B) is true i.e segment B'D' will run through (2,2) and will be longer than the segment BD.

Learn more about dilation from brainly.com/question/12528454

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