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Chapter 1: Problem 57

Sketch the straight line defined by the linear equation by finding the \(x\) - and \(y\) -intercepts. $$ 3 x-2 y+6=0 $$

Short Answer

Expert verified
The x-intercept is at point (-2, 0) and the y-intercept is at point (0, 3). Plot these points on a coordinate plane and connect them with a straight line to sketch the graph of the linear equation \(3x - 2y + 6 = 0\).

Step by step solution

01

Finding the x-intercept

To find the x-intercept, we set y = 0 and solve for x: $$ 3x - 2(0) + 6 = 0 $$ We simplify the equation and solve for x: $$ 3x + 6 = 0 $$ $$ 3x = -6 $$ $$ x = \frac{-6}{3} $$ $$ x = -2 $$ The x-intercept is at point (-2, 0).
02

Finding the y-intercept

To find the y-intercept, we set x = 0 and solve for y: $$ 3(0) - 2y + 6 = 0 $$ We simplify the equation and solve for y: $$ -2y + 6 = 0 $$ $$ -2y = -6 $$ $$ y = \frac{-6}{-2} $$ $$ y = 3 $$ The y-intercept is at point (0, 3).
03

Sketching the graph

To sketch the graph of the linear equation, plot the x-intercept point (-2, 0) and the y-intercept point (0, 3) on a coordinate plane. Connect these two points with a straight line. The line represents the graph of the given linear equation \(3x - 2y + 6 = 0\).

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