Question

Which one would the equation be?

Answer 1

Answer:

a. $y = \frac{2}{5}x - 6$

Step-by-step explanation:

The slope-intercept form of equation of a line is given as $y = mx + b$. Where,

m = slope

b = y-intercept.

Rewrite the equations, $2x - 5y = 12$ and $4y + 24 = 5x$, in the slope-intercept form by making y the subject of the formula. Then, derive our new equation that has the same slope as the first equation, and the same y-intercept as the second equation.

$2x - 5y = 12$

$2x - 12 = 5y$

Divide both sides by 5

$\frac{2x - 12}{5} = \frac{5y}{5}$

$\frac{2x}{5} - \frac{12}{5} = y$

Rewrite

$y = \frac{2x}{5} - \frac{12}{5}$

The slope of $2x - 5y = 12$ is ⅖.

$4y + 24 = 5x$

$4y = 5x - 24$ (subtraction property of equality)

Divide both sides by 4

$\frac{4y}{4} = \frac{5x - 24}{4}$

$y = \frac{5x}{4} - \frac{24}{4}$

$y = \frac{5x}{4} - 6$

The y-intercet of $4y + 24 = 5x$ is -6

Therefore, the equation that has the same slope as the first equation and the same y-intercept as the second equation would be:

$y = mx + b$

Plug in the values of m and b

$y = \frac{2}{5}x + (-6)$

$y = \frac{2}{5}x - 6$