What is the equation of the line that passes through the points (-4,3) and (2,-6)
1 answer:
Answer: y = -1.5x - 3
Step-by-step explanation:
We'll assume this is a straight line, with the form y=mx+b. m is the slope (the rate that y changes with a change in x) and b is the y-intercept (the value of y when x=0).
Once we can determine both m and b, we'll have an equation that answers this question. First, m.
m, the slope, is known as the Rise/Run. We can use the two given points to calculate this value. Take the two points, (-4,3) and (2,-6), and calculate the change in x (the Run), by subtrating the initial point (I'll choose (-4,3)) from the final point ((2,-6)). For x that is: 2-(-4) = 6. For y: -6-3 = -9. When x moved +6 units, y went down by 9, or -9. The slope is the Rise (-9) over the Run (6), or (-9/6). The slope of this line is - 1.5.
We now have y = -1.5x + b. To find b, use wither of the two points. I'll use (2,-6) because I like even numbers, but fell free to use the other. Both will give the same answer for b. [Try it].
Using (2,-6), we get:
y = -1.5x + b
-6 = -1.5*(2) + b
-6 = -3 + b
b = -3
The equation is y = -1.5x - 3
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For fun, try the other point, (-4,3) to find the value of b:
y = -1.5x + b
3 = -1.5*(-4) + b
3 = 6 + b
b = -3 The Same!
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The correct match of each tile of the equation with its solution is:
- n - 13 = - 12 →→→ 1
- n/5 = -1/5 →→→ -1
- n + 15 = - 10 →→→ -25
To match each tile to the correct box, we have to solve the arithmetic operations in the box, then drag the correct tile that matches our answer into the box.
From the image attached below;
1.
n - 13 = - 12
Let us add (+13) to both sides to eliminate (-13), i.e.
n - 13 + 13 = - 12 + 13
n = 1
2.
n/5 = -1/5
multiply both side by 5
n/5 × (5) = -1/5 × (5)
n = -1
3.
n + 15 = - 10
n +15 - 15 = - 10 - 15
n = -25
Learn more about matching each tile to the correct box here:
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