Write an equation in y=mx+b form

Question

Write an equation (y=Mx+b form) of the line passing through the point (-10,3) that is PARALLEL to the line 5x+2y=12.

write an equation of the line passing through the point (5,1) that is PERPENDICULAR to the line 5x+3y=15.

Answer 1

The slope of a line parallel to a given line is equal to the slope of the given line;

the slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line.

With this information you should be able to answer the question.

Answer 2

Mary,

If two lines are parallel to each other, they both have the same slope. So let us find the slope we are looking for:

5x + 2y = 12

2y = -5x + 12

y = -5/2x + 6

We want a line with slope -5/2, and it has to pass through (-10,3).

We can plug in this given point to solve:

3 = -5/2(-10) + ?

3 = 25 + ?

28 is our answer for that last question and so it is our y-intercept.

So the equation of our first line is y = -5/2x - 22

If two lines are perpendicular, their slopes are negative reciprocals of each other. So first find the slope of the first line:

5x + 3y = 15

3y = -5x + 15

y = -5/3x + 5

Your slope is -5/3 and the negative reciprocal of that is 3/5.

So we are looking for a line with slope 3/5 that goes through point (5,1).

Lets plug this point in, just like last time:

y = mx + b

1 = 3/5(5) + b

1 = 3 + b

b = -2

So the equation of this line is y = 3/5x - 2.

Hope this helps! :)

Answer 3

Write an equation (y=Mx+b form) of the line passing through the point (-10,3) that is PARALLEL to the line 5x+2y=12.

Parallel lines have same slope. Slope of 5x+2y=12 is

2y = 12 -5x

y = (-5/2)x + 12

then slope (M) is -5/2

So, our equation should have M = -5/2

y = (-5/2) x + b. Also, when x=-10, y must be 3. Substitute these values in the equation

3 = (-5/2) (-10) + b

3 = 25 + b

b = 3 - 25 = -22

write an equation of the line passing through the point (5,1) that is PERPENDICULAR to the line 5x+3y=15.

Perpendicular lines have a slope with the opposite sign and reciprocal. In other word, if one line has slope M, the perpendicular line has slope -1/M.

Let's find slope of 5x + 3y = 15

3y = -5x + 15

y = (-5/3)x + 5

So, slope M = -5/3. Then our equation is

y = (+3/5)x + b and needs to pass through x=5 and y = 1. Substitute:

1 = (3/5) * 5 + b

b = 1 - 3 = -2