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Question

What is an equation for the line with slope The fraction two thirds.and y-intercept 9? (1 point)
y = The fraction two thirds times x.x
y = 9x
y = The fraction two thirds times x.x + 9
y = 9x + The fraction two thirds.


6. What is an equation in slope-intercept form for the line that passes through the points (1, –3) and (3, 1)? (1 point)
y = 3x + 1
y = x – 3
y = 2x + 5
y = 2x – 5

Answer 1

The slope of a line is the ratio of the increase in y-values divided by the increase in x-values.  It is often called "rise over run."  The line with a slope of 2/3 will increase 3 units in the y direction for each 2 units in the x direction.

 

The y-intercept is the point on the line where it crosses the y-axis.  That means that the x-value at that point is 0.

 

The slope-intercept form of the equation of a line looks like this:    y=mx+b

     where m is the slope and b is the y-intercept [that is, the point (0,b)]

 

The line with slope 2/3 and y-intercept of 9 has equation  y=(2/3)x + 9

 

 6. What is an equation in slope-intercept form for the line that passes through the points (1, –3) and (3, 1)? (1 point)
 

The slope (remember, "rise over run") of this line is    ( (1-(-3)) / (3-1) )   =   4/2   =   2

          so, the equation so far is    y=2x + b             now we use either point to find the value of b

         -3 = 2(1) + b

          -5 = b

 

The equation of this line is:    y = 2x - 5

Answer 2

An equation of a line is written in the form  y=mx+b , where m is slope and b is y-intercept.

 

m = 2/3

 

b = 9

 

y = (2/3)x + 9

 

 

 

6)

 

Find the slope between the two points.

 

m = (y₂ - y₁) / (x₂ - x₁)

 

m = (1 - (-3)) / (3 - 1)

 

m = 4 / 2

 

m = 2

 

 

Next, we plug in the slope and the point (3,1) into the slope-intercept from of the line to find b.

 

y = mx + b

 

1 = 2(3) + b

 

1 = 6 + b

 

-5 = b

 

 

Your equation of the line is

 

y = 2x - 5

Answer 3

1. y = 2/3*x + 9 

 

2. y = 2x-5