Question

Amira is told there is a trick to finding the slope within an equation in standard form, Ax+By=C. She is told she can rewrite this equation in slope-intercept form, y=mx+b, to find the pattern. She correctly rewrites the equation 7x+9y=14 in slope-intercept form as y=− 7/9x +14/9. Which answer explains the pattern for how to find the slope using an equation in standard form?

A. In slope-intercept form, the slope is 14/9. These values are C and A, but with the opposite sign, so the slope of the line from the equation in standard form is − C/A.

B. In slope-intercept form, the slope is − 7/9. These values are A and B, but with the opposite sign, so the slope of the line from the equation in standard form is − A/B.

C. In slope-intercept form, the slope is 14/9. These values are C and B, but with the opposite sign, so the slope of the line from the equation in standard form is − C/B.

D. In slope-intercept form, the slope is − 7/9. These values are A and B, but with the opposite sign, so the slope of the line from the equation in standard form is − B/A.

Answer 1

B. In slope-intercept form, the slope is − 7/9. These values are A and B, but with the opposite sign, so the slope of the line from the equation in standard form is − A/B.

Explanation:

Let's convert the standard equation into slope-intercept form:

• Ax + By = C ⇒ subtract Ax from both sides
• By = -Ax + C ⇒ divide both sides by B
• y = -A/Bx + C/B ⇒ converted to slope- intercept form

As we see the slope is -A/B

The equation 7x + 9y = 14 is converted as:

• y = -7/9x + 14/9, where the slope is -7/9

Looking at the answer options and the correct one is option B, where both identification of slopes match.

• B. In slope-intercept form, the slope is − 7/9. These values are A and B, but with the opposite sign, so the slope of the line from the equation in standard form is − A/B.