Answer:
a. [tex] y = \frac{2}{5}x - 6 [/tex]
Step-by-step explanation:
The slope-intercept form of equation of a line is given as [tex] y = mx + b [/tex]. Where,
m = slope
b = y-intercept.
Rewrite the equations, [tex] 2x - 5y = 12 [/tex] and [tex] 4y + 24 = 5x [/tex], 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.
[tex] 2x - 5y = 12 [/tex]
[tex] 2x - 12 = 5y [/tex]
Divide both sides by 5
[tex] \frac{2x - 12}{5} = \frac{5y}{5} [/tex]
[tex] \frac{2x}{5} - \frac{12}{5} = y [/tex]
Rewrite
[tex] y = \frac{2x}{5} - \frac{12}{5} [/tex]
The slope of [tex] 2x - 5y = 12 [/tex] is ⅖.
[tex] 4y + 24 = 5x [/tex]
[tex] 4y = 5x - 24 [/tex] (subtraction property of equality)
Divide both sides by 4
[tex] \frac{4y}{4} = \frac{5x - 24}{4} [/tex]
[tex] y = \frac{5x}{4} - \frac{24}{4} [/tex]
[tex] y = \frac{5x}{4} - 6 [/tex]
The y-intercet of [tex] 4y + 24 = 5x [/tex] 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:
[tex] y = mx + b [/tex]
Plug in the values of m and b
[tex] y = \frac{2}{5}x + (-6) [/tex]
[tex] y = \frac{2}{5}x - 6 [/tex]
