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2 years ago

Can someone find the slope of these points- (8,20) and (4,61)

Mathematics

2 answers:

tino4ka555 [31]2 years ago

7 0

The equation for a slope is y2 - y1/x2-x1

61-20/4-8

41/-4

Archy [21]2 years ago

7 0

Answer:

The slope -41/4.

Step-by-step explanation:

Slope formula:

$\displaystyle \frac{Y_2-Y_1}{X_2-X_1}$

$\displaystyle \frac{61-20}{4-8}=\frac{41}{-4}=-\frac{41}{4}$

Therefore, the slope is -41/4, and the correct answer is -41/4.

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NO LINKS!! Use the method of substitution to solve the system. (If there's no solution, enter no solution). Part 11z

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Answer:

$(x,y)=\left(\; \boxed{-1,-8} \; \right)\quad \textsf{(smaller $x$-value)}$

$(x,y)=\left(\; \boxed{5,16} \; \right)\quad \textsf{(larger $x$-value)}$

Step-by-step explanation:

Given system of equations:

$\begin{cases}y=x^2-9\\y=4x-4\end{cases}$

To solve by the method of substitution, substitute the first equation into the second equation and rearrange so that the equation equals zero:

$\begin{aligned}x^2-9&=4x-4\\x^2-4x-9&=-4\\x^2-4x-5&=0\end{aligned}$

Factor the quadratic:

$\begin{aligned}x^2-4x-5&=0\\x^2-5x+x-5&=0\\x(x-5)+1(x-5)&=0\\(x+1)(x-5)&=0\end{aligned}$

Apply the zero-product property and solve for x:

$\implies x+1=0 \implies x=-1$

$\implies x-5=0 \implies x=5$

Substitute the found values of x into the second equation and solve for y:

$\begin{aligned}x=-1 \implies y&=4(-1)-4\\y&=-4-4\\y&=-8\end{aligned}$

$\begin{aligned}x=5 \implies y&=4(5)-4\\y&=20-4\\y&=16\end{aligned}$

Therefore, the solutions are:

$(x,y)=\left(\; \boxed{-1,-8} \; \right)\quad \textsf{(smaller $x$-value)}$

$(x,y)=\left(\; \boxed{5,16} \; \right)\quad \textsf{(larger $x$-value)}$

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