What are the slope and y-intercept of 2x − 3y + 9 = 0?
Answer and explanation
Correct answer: slope = 2/3, y-intercept = 3
Use the slope-intercept form y = mx + c. From 2x − 3y + 9 = 0, move the other terms to isolate the y-term: −3y = −2x − 9. Dividing by −3 gives y = (2/3)x + 3. Thus the coefficient of x is the slope m = 2/3, and the constant c = 3 is the y-intercept. Hence option A is correct. Option B results from losing the sign while dividing, whereas options C and D confuse the original coefficients or constant with the values in slope-intercept form. Substitution also checks the result: when x = 0, y = 3, satisfying the original equation.
Frequently asked questions
What is the correct answer to this question?
slope = 2/3, y-intercept = 3
Why is this the correct answer?
Use the slope-intercept form y = mx + c. From 2x − 3y + 9 = 0, move the other terms to isolate the y-term: −3y = −2x − 9. Dividing by −3 gives y = (2/3)x + 3. Thus the coefficient of x is the slope m = 2/3, and the constant c = 3 is the y-intercept. Hence option A is correct. Option B results from losing the sign while dividing, whereas options C and D confuse the original coefficients or constant with the values in slope-intercept form. Substitution also checks the result: when x = 0, y = 3, satisfying the original equation.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Slope and y-intercept.
