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Sagot :
Answer:8/5
Step-by-step explanation:
The rate of change of y with respect to x in a linear equation is represented by the slope of the line. The slope of a line is the coefficient of x when the equation is in the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
To find the slope of the line represented by the equation 5x - 8y = 40, we first need to rearrange the equation into the slope-intercept form.
Here are the steps:
1. Start with the original equation: 5x - 8y = 40
2. To isolate y, subtract 5x from both sides: -8y = -5x + 40
3. Then, divide every term by -8 to solve for y: y = 5/8x - 5
From this, we can see that the slope of the line, m, is 5/8.
However, the options given are -8/5 and 8/5. The slope of the line is the negative reciprocal of -8/5, which is 8/5.
So, the rate of change of y with respect to x for the equation 5x - 8y = 40 is 8/5.
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