Work out 5/5, r. Determine the equation of A(6,4) B(2,0)

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ScanSolve AI Tutor · Accepted Answer

Let's solve the problems from the image.

: Work out $\frac{5^4}{5^4}$

Apply the rule of exponents for division, which states that $\frac{a^m}{a^n} = a^{m-n}$ .
$\frac{5^4}{5^4} = 5^{4-4}$
Simplify the exponent.
$5^{4-4} = 5^0$
Any non-zero number raised to the power of 0 is 1.
$5^0 = 1$
The value is $\boxed{1}$ .

: Determine the equation of the line passing through (6, 4) and (2, 0)
Calculate the slope ( $m$ ) of the line using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ .
Let $(x_1, y_1) = (6, 4)$ and $(x_2, y_2) = (2, 0)$ .
$m = \frac{0 - 4}{2 - 6}$ $m = \frac{-4}{-4}$ $m = 1$
Use the slope-intercept form of a linear equation, $y = mx + c$ .
Substitute the slope $m=1$ into the equation.
$y = 1x + c$ $y = x + c$
Substitute one of the points into the equation to find the y-intercept ( $c$ ).
Let's use point $(2, 0)$ .
$0 = 2 + c$ $c = 0 - 2$ $c = -2$
Write the final equation of the line using the calculated slope and y-intercept.
$y = x - 2$
The equation of the line is $\boxed{y = x - 2}$ .

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