What line passes through the point (10,-1) and has a slope of -2?

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caledon | High School Teacher | (Level 3) Senior Educator

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Having a slope of -2 means that the rise-over-run is equivalent to -2/1, or a decrease of 2 Y units for every increase of 1 X unit. Basically, any rise-over-run fraction which gives a result of -2 will be a valid solution for this line.

The easy way to solve this is to use y = mx + b, where m is the slope and b is the Y intercept. We already have the slope, so y = -2x + b. We just need to find the Y intercept, i.e. X = 0. We can do this easily by simply counting down in integer increments from the slope values established above.

At (10, -1), we are 10 units away from a Y-intercept (where X = 0 and the line hits the Y axis). We can simply rearrange the rise-over-run expression to give X units of -10:

Y/-10 = -2

So the Y intercept will be 20 units away from -1, giving +19, and the equation is Y = -2x + 19

We can insert the original values to demonstrate:

-1 = -2(10) + 19

 

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caledon | High School Teacher | (Level 3) Senior Educator

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Durbanville has kindly pointed out that in the second paragraph, where I define a Y intercept, I state that Y=0; it is in fact X=0

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durbanville | High School Teacher | (Level 2) Educator Emeritus

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As a different approach from that stated above, use the information given where (10; -1) means that when x=10, y=-1.

The slope (m in the equation) is represented by -2 (given)

The y- intercept (which is where x=0), is represented by the b (from y =mx+b) 

To avoid confusion, please note that on the y intercept x=0 (always) and on the x intercept, y=0(always)

Substitute into y=mx +b at the point given (10; -1) 

`therefore -1 = (-2)(10) +b `

`therefore -1= -20 +b `

`therefore b= -1+20 = 19`

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So we also now know that (0;19) is a point on this graph. 

Ans: Therefore y=-2x+19

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nisarg | Student, Grade 11 | (Level 1) Valedictorian

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What line passes through the point (10,-1) and has a slope of -2?

 So we know Y=-2x+b where b is the intercept so plug in the point
-1=-20+b
then solve for b
 
-1=-20+b
19=b
 
So Y=-2x+19
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udonbutterfly | Student, College Freshman | (Level 1) Valedictorian

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So we are going to be using the slope intercept form which is y=mx+b

y and x are going to be your points/ coordinates.

m is the slope

b is what we are going to be looking for in order to find the equation for the line that passes through the point.

So 10 is x and -1 y and m is -2 we are going to substitute these into the equation

-1 = -2 x(10) + b So multiply the -2 by the 10

-1 = -20 + b Now add 20 on both sides

19 = b

So we are now going to rewrite the equation without the coordinates but the variables while replacing b with 19 so...

y=-2x + 19 This is the answer!

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tonys538 | Student, Undergraduate | (Level 1) Valedictorian

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The general formula for the equation of a line passing through a point (a, b) and with slope m is (y - b)/(x - a) = m

To derive the equation of a line passing through the point (10,-1) and with slope -2, substitute these values in the formula given.

(y - (-1))/(x - 10) = -2

(y + 1)(x - 10) = -2

y + 1 = -2*(x - 10)

y + 1 = -2x +20

2x + y - 19 = 0

The required equation is 2x + y - 19 = 0

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rachellopez | Student, Grade 12 | (Level 1) Valedictorian

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The equation for a line is y=mx+b where m is the slope and b is the y-intercept. Since you are given the slope you can simply plug in the numbers. Your equation is y=-2x+b, however, you have to solve for b. To do this, you use the point you are given and plug in the numbers for x and y. x=10 and y=-1.

(-1)=-2(10)+b

(-1)=-20+b

b=19

Now you can insert b into your equation and your final answer is y=-2x+19

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