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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
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
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
What line passes through the point (10,-1) and has a slope of -2?
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!
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
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.
Now you can insert b into your equation and your final answer is y=-2x+19
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