an equation in the slope-intercept form for the line passing through points (3,5) and(8,15)?

Answer 1

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Answer 2

Slope-intercept form is when an equation is in the form of y=mx+b, with m being the slope of the line (rise over run) and b being where the line intercepts (hits, connects) with the y-axis.
So the first thing you want to do is get the slope of a line that passes through those two given points.
To do this, use this formula:
y2-y1
divided by
x2-x1
It doesn't matter which points you designate as 2 and 1, but make sure if you pick the first set of points as (x1,y1) to stick with that for the other set.
So you have:
(15-5)/(8-3)
This gets you: 10/5 or 2.
So you have your slope (m) for the equation: 2.
Next, solve for the y-intercept (b). Go back to slope-intercept formula and plug in the variables that you know.
So you have y=2x+b.
Pick either pair of points (3,5) or (8,15) and plug them in for x and y.
Let's say we pick (3,5). Your equation now looks like this:
(5)=2(3)+b.
Simplify and solve for b. You have: 5=6+b.
To solve for b, isolate it by subracting 6 from both sides of the equal sign. You are now left with b=-1.
Substitute your newly found slope (m) and y-intercept (b) of 2 and -1, respectively.
So your final answer is:
y=2x-1

Hope this helps!

Answer 3

Insteading of memorizing ten different formulas just memorize the deffinition of slope:

slope = m = rise/run = (y2-y1)/(x2-x1)

Now consider the line through the two points given in your problem. The slope through either of the points and the point (x,y) representing any point on the line is constant. The slope through (3,5) and any point (x,y) is just rise/run calculatied as shown above to give

m = (y-5)/(x-3)

But we can calculate a numerical value for this slope using both points:

m = (15-5)/(8-3) = 10/5 = 2

So let's set the slopes equal and then solve for y:

(y-5)/(x-3) =2/1 Cross mltiplying to eliminate fractions

y-5 = 2x - 6

y = 2x -1

Notice in this last equation the slpe 2 is the coeficient of x and when x=0 y= -1 so -1 must be the y intercept.

So y = 2x - 1 is the slope intercept form of your line.

Answer 4

slope intercept form --> y = mx + b the place m is the slope of the line and b is the y intercept. the y intercept is the place the line crosses the y (vertical) axis. i will locate the slope and the y intercept with this equation form to try this subject you first have you ever use a diverse form of equation. it relatively is noted as element slope form. It makes use of a element on the line, and the slope element slope form --> (y - y1) = m(x - x1) the place m is the slope and (x1, y1) is a element on the line (y - 4) = (-a million)(x - (-5)) --> i basically inserted (- 5, 4) for x1 and y1, and m = -a million into the equation. there are countless negatives on the x ingredient, so we could take it one step at a time y - 4 = (-a million) ( x + 5) --> now distribute the (-a million) slope y - 4 = - x - 5 --> upload 4 to the two sides y = - x - a million --> it is slope intercept form. the coefficient of x is the slope and m = -a million the y intercept is the selection further or subtracted from x, b = -a million

Answer 5

Just use the two points given to calculate the slope by using:
(15-5)/(8-3) = 10/5 = 2, so your slope is 2.
Then use the standard formula y=mx+b and plug in y and x using one of the points given and the slope you just got (for m) and solve for b. I used the point (3,5) along with the slope we just got m=2 :
5=2(3)+b, after solving you get b= -1
then put b and m into the standard equation and your done:
y=2x-1

Answer 6

ok so the formula for an equation in slope-intercept form is
y=mx+b where m is the slope and b is the y intercept.

so first let's find m (the slope)

slope is (y2-y1) / (x2-x1)

(3,5) this is in the format (x1,y1)
(8,15) this is in the format (x2,y2)

So slope is (15-5) / (8-3)
10/5
2

So your slope is 2. This is your m so plug this into the equation.

y=mx+b
y=2x+b

Now we need to figure out what b is.

Just plug in one of the points they gave you to figure this out.

Let's pick (3,5) which is in (x,y) form. So x=3 and y=5. Plug these into your equation y=2x+b.

5=2(3)+b
5=6+b
solve for b
subtract 6 from both sides
b= -1

Plug this back into your equation
y=2x+b
y=2x+(-1)

y=2x-1

Answer 7

slope-intercept form: y=mx+b
m = slope slope is rise/run or if negative down/left
b = y-intercept
m = (y2 - y1) / (x2 - x1) = (15-5) / (8-3) = 10/5 = 2
change the slop to still equal 2 but have the (x) part be 3
m = 6/3
b = (3,5) 3 - 3 = 0 5 - 6 = -1 (0,-1)

answer:
y = 2x - 1

Answer 8

m=y2-y1/x2-x1 >>>>m=15-5/8-3=10/5=2 >>>m=2
y=mx+b>>>>>>>substitute.....take one of the points...I will use the first one because seems easy to solve....5=2(3)+b
we are looking for "b" 5=6+b subtract 6 on both sides
5=6+b
-6 -6 -1=b now you can make a equation
y=2x-1 that's your equation of the two points...(3,5), (8, 15)

Answer 9

m = (15 - 5) / (8 - 3) = 10 / 5 = 2
y - 5 = 2(x - 3)
y = 2x - 6 + 5
y = 2x - 1

Answer 10

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