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 /.
Answer -
Slope of the line passes through two points P(x1 , y1 ) and Q (x2 , y2 ) is given by—
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 to—
 -2/ -7
 2/7
 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 as—
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 as—
-3=y
By taking LCM (3) on the left hand side, we get—
=y
This equation can be further written in simplest form as---
2x-9=3y
In the standard form, it can be written as—
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.

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