x, y, slope

Question

Given the function 2x+y=7 find the following:

a. X-intercept

b. Y- intercept

c. Slope

Answer 1

put the equation in slope intercept form by subtracting 2x from both sides 

 

y=-2x+7. 

Now you have the answer to parts b and c. The slope is -2 and the y intercept is 7 which can be written as (0,7).

 

To find the answer to part a, you set y=0 and solve for x. 

2x+0=7 from the original equation so dividing both sides by 2,

x=7/2 and written as (7/2,0)

Answer 2

In problems of this kind, SOLVE FOR y!

 

Then your specific equation will have particular values for m (slope), the coefficient of x, and b, the y-intercept.

 

For example 10x + 5y = 20 leads to y = -2x + 4 so slope is -2 and the y-intercept b=4, i.e. the coordinates of the y-intercept are (0,4).

 

Just apply this knowledge* to your particular equation.

 

To find the x-intercept, substitute 0 for y and determine what the x value is!

 

* All of this information is classified as MUST BE UNDERSTOOD & RETAINED for future success in all Math!

Answer 3

Let's start by rewriting the equation to isolate y (y = mx + b):

subtract 2x from both sides:

y = -2x + 7

 

We find the x intercept by setting y = 0 and finding x:

0 = -2x + 7

-7 = -2x

-7 / -2 = x

x = ⁷/₂, or 3 ¹/₂

 

The y-intercept is our b variable, so that's 7.

(We set x = 0. y = 0 + 7. y = 7)

 

The slope is the coefficient connected to the x variable, so that's -2.

 

Answer 4

Ryan,

 

The equation in the form given is the standard form.  The slope intercept for is the most useful to find y-intercept and slope.

 

For the x-intercept, set y=0 and solve

2x+y=7

2x+0 = 7

x = 7/2

 

For the y-intercept, set x=0 and solve

2x+y=7

2(0) + y = 7

y=7

Note also the following

2x+y=7

y = -2x+7

y-intercept = 7

 

And finally, the slope = -2