I have to take a college placement test and am studying the practive test. He is the question . . . What is the equation of the line that contains the points with (x,y) coordinates (-3,7) and (5,-1)? I know that the answer is y=-x+4, but I cannot remember from high school what I do to find the answer. What is the formula?
There are various ways. One is to first get the slope m using
(x1,y1) = (-3, 7) (x2,y2) = (5,-1)
m = (y2 - y1)/(x2 - x1) = -8/8 = -1
The equation for the line can be written by forcing it to go through the point (x1,y1) with slope m:
(y - y1) = m (x - x1)
y -7 = (-1)*(x + 3)= -x -4
y = -x + 3
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the pair of equation 7x+ky=k,14x+2y=k=1 represent coincident lines
To find the equation of a line that contains two points, you can follow these steps:
1. Identify the coordinates of the two points given. In this case, the points are (-3,7) and (5,-1).
2. Use the formula for slope (m) to find the slope of the line. The slope formula is:
m = (y2 - y1)/(x2 - x1)
Let's label the coordinates as follows:
(x1, y1) = (-3,7)
(x2, y2) = (5,-1)
Plugging these values into the slope formula:
m = (-1 - 7)/(5 - (-3))
= (-1 - 7)/(5 + 3)
= (-8)/(8)
= -1
Therefore, the slope of the line is -1.
3. Now that we have the slope (m), we can use the point-slope form of a line to find the equation. The point-slope form is:
(y - y1) = m(x - x1)
Using the point (x1, y1) = (-3,7) and the slope (m) = -1:
(y - 7) = -1(x - (-3))
= -1(x + 3)
4. Simplify the equation by distributing -1 to both terms inside the parentheses:
(y - 7) = -x - 3
5. Reorder the equation to isolate y:
y = -x - 3 + 7
= -x + 4
Therefore, the equation of the line that contains the points (-3,7) and (5,-1) is y = -x + 4.