Find the equation of the line, which makes intercepts -3 and 2 on the x- and y-axes respectively.
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Step-by-Step Solution
Step 1: Identify the intercepts
The problem states that the line makes an x -intercept of −3 and a y -intercept of 2. We denote the x -intercept as a and the y -intercept as b.
Step 2: Recall the intercept form of a line
The intercept form of the equation of a straight line is given by ax+by=1, where a is the x -intercept and b is the y -intercept.
Step 3: Substitute the intercept values
Now, substitute the given values of the x -intercept (a=−3) and the y -intercept (b=2) into the intercept form equation.
Step 4: Simplify the equation
To simplify, find a common denominator for the fractions, which is 6. Multiply the entire equation by 6 to eliminate the denominators. Then, rearrange the terms to get the equation in the standard form Ax+By+C=0.