Finding an equation in slope intercept form

[jamsey777]

Ok, another graphing question. I am woking on a problem that is wanting me to find and equation of the line through points (6, 2) and (8, 8) and it needs to be in slope intercept form. I'm confused simply because my book has been no help because any of the example ask you to find an equation for a problem that has a slope value and y-intercept. Slope intercept has to be solved using the formula y=mx+b. Any suggestions? Thank yoy for any help...

 

[Deleted member 4993]

Ok, another graphing question. I am woking on a problem that is wanting me to find and equation of the line through points (6, 2) and (8, 8) and it needs to be in slope intercept form. I'm confused simply because my book has been no help because any of the example ask you to find an equation for a problem that has a slope value and y-intercept. Slope intercept has to be solved using the formula y=mx+b. Any suggestions? Thank yoy for any help...

If a line goes through \(\displaystyle (x_1, y_1) and (x_2, y_2)\) - then the equation of the line is:

\(\displaystyle \frac{(y - y_1)}{(y_2 - y_1)} \ = \frac{(x - x_1)}{(x_2 - x_1)}\\)

Then simplify into y = mx + b form.

 

[jwpaine]

Ok, another graphing question. I am woking on a problem that is wanting me to find and equation of the line through points (6, 2) and (8, 8) and it needs to be in slope intercept form. I'm confused simply because my book has been no help because any of the example ask you to find an equation for a problem that has a slope value and y-intercept. Slope intercept has to be solved using the formula y=mx+b. Any suggestions? Thank yoy for any help...

\(\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}\)
\(\displaystyle y - y_1 = m(x - x_1)\)

Plug and chug, then simplify y in terms of x.
John

 

[nycfunction]

Ok, another graphing question. I am woking on a problem that is wanting me to find and equation of the line through points (6, 2) and (8, 8) and it needs to be in slope intercept form. I'm confused simply because my book has been no help because any of the example ask you to find an equation for a problem that has a slope value and y-intercept. Slope intercept has to be solved using the formula y=mx+b. Any suggestions? Thank yoy for any help...

Let's do it together. Ready?

You were given two points: (6, 2) and (8, 8).

We need to find the slope.

Let m = slope of the line.

We need the slope formula and here it is:

m = (x2 - x1)/(y2 - y1)....We plug and chug.

m = 8 - 2/8 - 6

m = 6/2

m = 3

Our slope is 3. By the way, the slope of any line is the rise over the run or simply put rise divided by the run, which is written slope = RISE/RUN.

Got it?

We now use a formula called the point-slope formula.

Here is the formula:

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

Take one of the points (your choice), plug the x and y coordinates of the point you chose and along with your slope (our slope is 3), simplify the formula.

I selected point (8, 8) but the other point will work just the same. We now PLUG AND CHUG again.

(y - 8) = 3(x - 8)

y - 8 = 3x - 24

Our goal is to ISOLATE y (place y all alone on one side of the equation).

y = 3x -24 + 8

y = 3x -16....This is your equation in slope-intercept form. Another way to say slope-intercept form is the y-intercept form. So, the equation y = 3x - 16 is written in the y = mx + b form.

EXTRA MATH FACTS:

Do you see number 3 in the equation we found? The number 3 here is the slope of this line.

Do you see -16? This number indicates where the line crosses (or touches) the y-axis on the xy-plane when x = 0. In other words, THIS line crosses the y-axis at the point (0, -16).

Is this clear?