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Math  /  Algebra

QuestionIf a>0a>0 and b>0b>0, which of the following could be an equation of the line graphed in the xyx y-plane below? y=−ax+by=-a x+b y=ax−by=a x-b y=abxy=a b x y=−ax−by=-a x-b y=ax+by=a x+b

Studdy Solution

STEP 1

1. The line has a negative slope.
2. The line crosses the y-axis above the origin.
3. The line crosses the x-axis to the right of the origin.
4. Both a a and b b are positive numbers.

STEP 2

1. Analyze the slope of the line.
2. Analyze the y-intercept of the line.
3. Determine which equation matches the given conditions.

STEP 3

The line has a negative slope, which means the coefficient of x x in the equation must be negative.

STEP 4

The line crosses the y-axis above the origin, which means the y-intercept must be positive.

STEP 5

Given the conditions, we need an equation where the coefficient of x x is negative and the constant term is positive.

STEP 6

Examine each option: - y=−ax+b y = -ax + b : Negative slope, positive y-intercept. - y=ax−b y = ax - b : Positive slope, negative y-intercept. - y=abx y = abx : Positive slope, no y-intercept term. - y=−ax−b y = -ax - b : Negative slope, negative y-intercept. - y=ax+b y = ax + b : Positive slope, positive y-intercept.
The equation y=−ax+b y = -ax + b satisfies both conditions: negative slope and positive y-intercept.
The equation that matches the conditions is:
y=−ax+b \boxed{y = -ax + b}

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