Consider the line y=6/7x-7 find the equation of the line that is perpendicular to the line and passes through the points (6,3)

find the equation of the line that is parallelto the line and passes through the points (6,3) ​

y = -7/6x + b

Step-by-step explanation:

Perpendicular lines require the reciprocal of the slope and opposite sign to the original slope. Then, you substitute the x and y coordinates into the equation to find the y-intercept. Done.

y = 6/7x -7     (6,3)

y = -7/6x + b

3 = -7/6(6) + b

3 = -7 + b

7     7

10 = b

y = -7/6x + b

see below

Step-by-step explanation:

If two lines are perpendicular to each other, they have opposite slopes.

The first line is y = 6/7x. Its slope is (6/7). A line perpendicular to this one will  have a slope of -7/6.

Plug this value (-7/6) into your standard point-slope equation of y = mx + b.

y = -7/6x + b

To find b, we want to plug in a value that we know is on this line: in this case, it is (6, 3). Plug in the x and y values into the x and y of the standard equation.

3 = -7/6(6) + b

To find b, multiply the slope and the input of x (6)

3 = -42/6 + b

3 = -7 + b

Now, add 7 to both sides to isolate b.

10 = b

Plug this into your standard equation.

y = -7/6x + 10

This equation is perpendicular to your given equation (y = 6/7x -7) and contains point (6, 3)

If two lines are parallel to each other, they have the same slope.

The first line is y = 6/7x - 7. Its slope is (6/7). A line parallel to this one will also have a slope of 6/7.

Plug this value (6/7) into your standard point-slope equation of y = mx + b.

y = 6/7x + b

To find b, we want to plug in a value that we know is on this line: in this case, it is (6, 3). Plug in the x and y values into the x and y of the standard equation.

3 = 6/7(6) + b

To find b, multiply the slope and the input of x (6)

3 = 36/7 + b

Now, subtract 36/7 to both sides to isolate b. To make this easier to visualize, convert 3 to have a denominator of 7.

21/7 - 36/7 = b

-15/7 = b

Plug this into your standard equation.

y = 6/7x - 15/7

This equation is parallel to your given equation (y = 6/7x - 7) and contains point (6, 3)

Hope this helps!

addition

step-by-step explanation: