<h2>
Answer: y = x + 1
</h2>
Step-by-step explanation:
For us to write the equation for this line, we need to (1) find the slope of the line, and (2) use one of the points to write an equation:
The question gives us two points, (3, 4) and (-4,-3), from which we can find the slope and later the equation of the line.
<u>Finding the Slope</u>
The slope of the line (m) = (y₂ - y₁) ÷ (x₂ - x₁)
= (4 - (- 3)) ÷ (3 - (-4))
= 1
<u>Finding the Equation</u>
We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:
⇒ y - (-3) = 1 (x - (-4))
y + 3 = (x + 4)
we could also transform this into the slope-intercept form ( y = mx + c)
since y + 3 = (x + 4)
⇒ y = x + 1
<em>To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.</em>
Answer:
C (if the sign after the digit 1,2,3,4 is not minus !!!)
Step-by-step explanation:
There are two ways to solve this question.
1) To solve this question, we need to substitute a = 6 and b = -3 into the given expression and then evaluate:
(-a)(b)(-a + b)
= (-6)(-3)(-6 + (-3))
= 18(-9)
= -162
2) An alternative method is to simplify (-a)(b)(-a + b) into an expression without brackets and then substitute a = 6 and b = -3:
1. (-a)(b)(-a + b)
= (-ab)(-a + b)
= -ab*(-a) + (-ab)*b
= a^(2)b+ (-ab^(2))
= a^(2)b - ab^(2)
2. a^(2)b - ab^(2)
= 6^(2)*(-3) - 6*(-3)^2
= 36*(-3) - 6*9
= -108 - 54
= -162
The key to either method is to be careful with placement of brackets, especially where there are negative values involved.
Let us set up some variables:
Now let us set up some equations based on the facts:
- length of rectangle is 4 times its width --> L = 4W
- perimeter of rectangle is 80 --> 2L + 2W = 80
Equations:
L = 4W -- equation 1
2L + 2W = 80 -- equation 2
Plug the value of L from equation 1 into equation 2
2(4W) + 2W = 80
8W + 2W = 80
10W = 80
W = 8 -- equation 3
Plug the value of W from equation 3 into equation 1:
L = 4W = 4 * 8 = 32
Therefore the length is 32 and the width is 8.
Hope that helps!