What is an equation for the points (5,-2) and (-16,4) in a slope intercept

Question

PLEASE!! answer my question! I have  a test and would like to know if I am correct????

Answer 1

First find the slope.  You know that the slope {Eqn 1} m =  (y2-y1) / (x2-x1).  The problem is giving you two coordinates, so you should be able to find the slope easily.

 

Next substitute the slope and coordinates of one point the slope intercept form and solve for b.

y = mx + b   {Eqn 2}

 

The m in the above equation is the slope that you found in the first step.  Plug it into equation 2.  You now have y, m and x.  And you're left with figuring out b.  One equation, one unknown.  You should be able to find b easily.

 

The slope-intercept form of the equation of the line requires you to substitute the slope m and the y-intercept b that you found when you solved Eqn 1 and 2 into the eqn y = mx + b.  So you're final answer will look something like y = 4x + 7 (although note that I just randomly picked the numbers 4 and 7.  I'm leaving it up to you to find the m and b values for this problem).  I know you can do it !  Once you have solve the problem, if you want to run it by me to double-check, please do so.

 

Answer 2

y = -2x/7 -4/7

Answer 3

Hello Michelle!

 

I am happy to help you with your question.

 

Here's an explanation:

The slope-intercept form of an equation is the form y = mx + b, where m is the slope and b is the y-intercept. So, to find the equation, you'll need to find both of these values.

 

First, to find slope, use the equation (y2 - y1)/(x2 - x1). Using the points that you gave, this would look like (4 - (-2)) / (-16 - 5). When you simplify these values, you should get 6/-21 which will reduce to -2/7.

 

Next we'll find the y-intercept. Just plug in the slope you found above and the values from one of your coordinate points and solve for b.

 

Let's use the point (5, -2)

Then,                 y = mx + b

                        -2 = (-2/7)(5) + b

                        -2 = -10/7 + b

                        -2 + 10/7 = -10/7 + 10/7 + b

                        -4/7 = b

 

So, since b = -4/7, the final equation in slope-intercept form is: y = -2/7x - 4/7.

 

If you liked this explanation, I hope you'll consider contacting me, Andrea Brant, for additional tutoring help in the future. I wish you great luck on your test!! Have a wonderful evening.

 

Andrea

Answer 4

Using two-point form:

 

(y - (-2)) / (x - 5) = (-2 - 4) / (5 - (-16))

(y + 2) / (x - 5) = -6 / 21

21(y + 2) = -6(x - 5)

21y + 42 = -6x + 30

21y = -6x - 12

y = -6x/21 - 12/21

y = -2x/7 - 4/7

Answer 5

First, we need the slope of the line: m = (y2 - y1)/(x2 - x1) = (4 - {-2})/(-16 - 5) = 6 / -21 = - 2/7.

Then use either point to form the equation y - y2 = m(x - x2).

Using the first point: y - (-2) = -2/7 ( x - 5);  y + 2 = -2/7 x + 10/7;  y = -2/7 x + 10/7 - 14/7;

y = -2/7 x - 4/7

or 2/7 x + y = - 4/7