Rewrite the equation $3 x-5 y=30$ in slope-intercept form.
a. $y=-\frac{2}{5} x+30$
b. $y=-\frac{5}{3} x-6$
c. $x=\frac{5}{3} y-6$
d. $y=\frac{3}{5} x-6$
Answer (2)
Isolate the y-term by subtracting 3 x from both sides: − 5 y = − 3 x + 30 .
Divide both sides by − 5 to solve for y : y = 5 3 x − 6 .
Express the equation in slope-intercept form: y = 5 3 x − 6 .
The equation in slope-intercept form is: y = 5 3 x − 6 .
Explanation
Understanding the Problem We are given the equation 3 x − 5 y = 30 and we want to rewrite it in slope-intercept form, which is y = m x + b , where m is the slope and b is the y-intercept.
Isolating the y-term First, we want to isolate the term with y on one side of the equation. We can subtract 3 x from both sides of the equation to get: − 5 y = − 3 x + 30
Solving for y Next, we want to solve for y by dividing both sides of the equation by − 5 :
− 5 − 5 y = − 5 − 3 x + 30 y = − 5 − 3 x + − 5 30 y = 5 3 x − 6
Identifying the Correct Option Now we have the equation in slope-intercept form, y = 5 3 x − 6 . Comparing this with the given options, we see that it matches option d.
Examples
Understanding slope-intercept form is useful in many real-world scenarios. For example, if you are tracking the cost of a taxi ride, the initial fee could be the y-intercept and the cost per mile could be the slope. By knowing these values, you can easily calculate the total cost of the ride for any distance. Similarly, in business, linear equations can represent revenue or cost functions, where the slope indicates the rate of change and the y-intercept represents the initial value.
To rewrite the equation 3 x − 5 y = 30 in slope-intercept form, we isolate y , yielding y = 5 3 x − 6 . This corresponds to option d. Therefore, the correct answer is d.
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