Rewrite the equation $3x - 5y = 30$ in slope-intercept form.
A. $y=-\frac{3}{5}x+30$
B. $y=-\frac{5}{3}x-6$
C. $x=\frac{3}{3}y-6$
D. $=-\frac{3}{5}<-6$
Answer (2)
Isolate the y-term: Subtract 3 x from both sides to get − 5 y = − 3 x + 30 .
Divide by the coefficient of y : Divide both sides by − 5 to get y = 5 3 x − 6 .
Identify the slope and y-intercept: The equation is now in the form y = m x + b .
State the final answer: 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 isolate the term with y on one side of the equation. We can subtract 3 x from both sides of the equation: 3 x − 5 y − 3 x = 30 − 3 x − 5 y = − 3 x + 30
Solving for y Next, we divide both sides of the equation by the coefficient of y , which is − 5 :
− 5 − 5 y = − 5 − 3 x + 30 y = − 5 − 3 x + − 5 30 y = 5 3 x − 6
Identifying Slope and Intercept The equation is now in slope-intercept form, y = m x + b , where m = 5 3 is the slope and b = − 6 is the y-intercept.
Final Answer Therefore, the equation in slope-intercept form is y = 5 3 x − 6 .
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 physics, if you are analyzing the motion of an object with constant velocity, the initial position could be the y-intercept, and the velocity could be the slope, allowing you to predict the object's position at any time.
To rewrite the equation 3 x − 5 y = 30 in slope-intercept form, we isolate the y term and divide by the coefficient of y . The correct form is y = 5 3 x − 6 . None of the provided multiple-choice options is accurate as the equation is expressed correctly as shown.
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