# Slope of a Line Equation

1. If line / goes through (1,3) and is parallel to the line through (4,3) and (-3,1). find the slope of /.

2. How do I write the equation y=2/3x-3 in standard form using only integers and a positive coefficient for x.

3. What is the equation if a line /goes through (-3,-1) and

(-1,4)?

4. What is the equation in slope-intercept form) of the line that goes through

(-1,2) and has slope 4?

https://brainmass.com/math/graphs-and-functions/slope-line-equation-257675

## SOLUTION This solution is **FREE** courtesy of BrainMass!

1. if line / goes through (1,3) and is parallel to the line through (4,3) and (-3,1). find the slope of /.

Answer -

Slope of the line passes through two points P(x1 , y1 ) and Q (x2 , y2 ) is given byâ€”

Slope=

Here, we have given two end points (4,3) and (-3,1) of a line.

Let us assume that slope of the line through (4,3) and (-3,1) is m1.

Thus, slope (m1) of the given line (4,3) and (-3,1) is ---

Slope (m1) = (1-3)/(-3-4))

which is equal toâ€”

ïƒ° -2/ -7

ïƒ° 2/7

ïƒ° 2/7

m1=2/7

According to the theorem, two lines are parallel if and only if they have equal slope

Thus, the line goes through (1,3) and the line through (4,3) and (-3,1) have equal slope.

Now, assume that the slope of the line goes through (1,3) is m2.

So, we can write the statement stated above asâ€”

m1 = m2 = 2/7

Thus, the slope of the line goes through (1,3) is 2/7

2. how do i write the equation y=2/3x-3 in standard form using only integers and a positive coefficient for x.

Answer -

Standard form of equation is

Ax+ By = C, where A,B and C are constants.

Now, y=2x/3-3 can be written asâ€”

-3=y

By taking LCM (3) on the left hand side, we getâ€”

=y

This equation can be further written in simplest form as---

2x-9=3y

In the standard form, it can be written asâ€”

2x-3y=9

3. what is the equation if a line /goes through (-3,-1) and

(-1,4)?

Answer -

Any line passing through the two points P(x1 , y1 ) and Q (x2 , y2 ) is given by:-

(y-y1 )= * (x - x1)

In your question (x1 , y1 ) is (-3 , -1) and (x2 , y2 ) is (-1 , 4).

The equation of the line passing through these points is

(y - (-1)) = * (x-(-3))

or (y +1) = * (x+3)

or (y +1) = * (x+3)

Cross Multiplying we have -

2y + 2 = 5x + 15

or 5x - 2y + 13 = 0 is the required equation.

4. what is the equation in slope-intercept form) of the line that goes through

(-1,2) and has slope 4?

Answer -

The slope-intercept form is given by,

y = mx + c

where, m is the slope of the line and c is the y-intercept.

or the other way of writing it is -

(y-y1 )= m (x - x1)

Where, m is the slope of the line.

Now we have (x1, y1) = (-1, 2) and slope = 4.

Using the above slope-intercept form, we have -

(y - 2) = 4(x - (-1))

(y - 2) = 4(x + 1)

y - 2 = 4x + 4

Adding 2 on both sides we have -

y - 2 + 2 = 4x + 4 + 2

y = 4x + 6.

This is the equation in the slope intercept form.

https://brainmass.com/math/graphs-and-functions/slope-line-equation-257675