3x +7y =21 with a y-intercept of (0, 2). Write the equation of the given line in slope-intercept form and determine its slope. equation: slope:

Question

1. Write the equation of a line perpendicular to the line 3x +7y =21 with a y-intercept of (0, 2). Write your answer in standard form.

Follow the steps below.

Step 1. Write the equation of the given line in slope-intercept form and determine its slope. 

equation:

slope:

Answer 1

In order to determine the equation of the line that is perpendicular to the given line, you need to determine the slope of the given line. You do that by transforming to slope-intercept from, i.e. y = mx + b (get the y variable by itself).

3x + 7y = 21

7y = -3x + 21 (subtract the term 3x from both sides; some say "drag" the term from left side to right side, and when you "drag" a term its sign is changed; that is just a mental image to use--you really are just subtracting from both sides).

y = (1/7) (-3x + 21) --divide both sides by the numerical coefficient of y; or multiply by its reciprocal.

y = -3x/7 + 3 -- use the distributive property for multiplication over addition

In this form you can identify the slope of the original line as -3/7. Note that the original post is incorrect. The y-intercept is at (0,3).

The slope of the perpendicular is 7/3 (the negative or opposite reciprocal of -3/7). We want the perpendicular line to have a y-intercept of (0,2). So we have m = 7/3 and b = 2. Just substitute into y = mx + b:

y = (7/3)x + 2 is the equation of the perpendicular.

Visit this Desmos graph to see that all lines with a slope of 7/3 are perpendicular to the original line:

desmos.com/calculator/lkv8t01hax

Answer 2

The given equation is 3x + 7y = 21.

To write it in slope-intercept form (y=mx+by = mx + b), follow these steps:

Step 1: Isolate the variable y from the equation 3x+7y=21

3x+7y=21

Subtract 3x from both sides:

7y=−3x+21

y = -3x + 21

Divide by 7:

y=−3/7x+3

Step 2: Identify Slope and Y-Intercept

The equation is now in slope-intercept form y=mx+b, where:

1. Slope (m) = −3/7
2. Y-intercept (b) = 3

Step 3: Verify Given Y-Intercept

The provided y-intercept is (0, 2), but from our conversion, the correct intercept is (0, 3). This suggests a possible mistake in the given data.

Final Answer:

The equation in slope-intercept form is:

y=−3/7x+3

And the slope is −3/7.

Note that -3/7 is a fraction.

Given that our slope (m) is -3/7, the slope of a perpendicular line is the negative reciprocal. That means negative becomes positive, and the reciprocal of 3/7 is 7/3.

Therefore, our slope is 7/3.

Now, using the y-intercept (0, 2) and the slope of the perpendicular line, 7/3, we can write the equation of the line in slope-intercept form (y = mx + b).

y=7/3x+2

To convert to standard form ax+by=c, we multiply 3 everywhere to eliminate the fraction:

3y=7x+6

Subtract 7x on both sides of the equal sign, and our equation in standard form is:

-7x+3y=6

Since the value of a should be positive, we can multiply both sides of the equal sign by -1. The equation in standard form will be:

7x-3y=-6

The final answer is 7x-3y= -6.

Answer 3

3x+7y = 21

7y = -3x +21

y = (-3/7)x + 3 is the equation in slope intercept form. slope = the coefficient of the x term = -3/7. intercept = the y intercept = the constant term = 3 = the point (0,3)

a perpendicular line has a negative inverse slope. take -3/7, flip it upside down and change its sign to get 7/3

y = (7/3)x +2 is the perpendicular line with y intercept = (0,2)

Answer 4

3x+7y=21 line and establish a perpendicular line through point (0,2)

is another way to look at problem

y=(-3/7)x+3 line

-3/7 slope

line perpendicular to y=(-3/7)x+3 through (0,2)

7/3=(y-2)/(x-0)

7x=3y-6

7x-3y=-6