a line has a slope of -2/3 for a pair of points on the line. Find the missing coordinate if the points are (-1,y) and (4,7)
1 answer:
Answer:
The missing co-ordinate is: (-1,).
Step-by-step explanation:
Given the slope of a line and a point on it, we determine the equation of the line by slope - one point form.
Slope - one point form: (y - y₁) = m(x - x₁)
Where, (x₁,y₁) is the point passing through the line.
Here the slope is and the point (x₁,y₁) = (4,7).
Therefore the equation would be:
y - 7 = (x - 4)
⇒ 3y - 21 = -2x + 8
⇒ 2x + 3y - 29 = 0 is the equation of the line.
Now it is given that (-1,y) also passes through the line, this point should satisfy the equation.
⇒ 2(-1) +3y = 29
⇒ 3y = 31 i.e., y =
Therefore, the missing co-ordinate is: (-1,).
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Answer:
(2, -2) and (1,-3)
Step-by-step explanation:
The y-intercept means that the coordinate where the line touches the y-axis. In other words, the y value(-4) when x=0. The result is (0, -4). The y coordinate also can be used to fill c variable of y=mx + c
We have 2 coordinates now, (3, -1) and (0, -4), then we can find out the line equation. We need to find the slope (m), the formula will be:
m= y2-y1 / x2-x1=
m= -4 - (-1) / (0-3)
m= -3/-3= 1
The line equation is:
y= mx + c
y= 1x + (-4)
y= x-4
After you have the equation, you can try to test the point individually to find if any of them fit the equation. You can also draw a line on the graph and see if any point touches the graph.
Red dot is the two point we have, red line is straight line that made from both point, and blue point is the option. As you can see on the graph, the points that touch the line will be (2, -2) and (1,-3)
