The equation of a line is given in slope-intercept form as \( y = 2x + 3 \). Find the x-intercept of this line.
["Understanding the Slope-Intercept Form: Finding the x-Intercept of ( y = 2x + 3 )", "When studying linear equations, one of the most useful forms is the slope-intercept form, given by the equation:\n[ y = mx + b ]\nHere, ( m ) represents the slope of the line, and ( b ) is the y-intercept — the point where the line crosses the y-axis.", "For the equation ( y = 2x + 3 ), we can directly identify:\n- Slope (( m )) = 2\n- Y-intercept (( b )) = 3", "But beyond identifying key features of a line, a common question in algebra is: What is the x-intercept?", "### What is the x-intercept?\nThe x-intercept occurs at the point where the line crosses the x-axis. At this point, the value of ( y ) is zero. Therefore, to find the x-intercept, we set ( y = 0 ) and solve for ( x ) using the equation.", "### Step-by-Step: Find the x-intercept of ( y = 2x + 3 )", "1. Set ( y = 0 )\n Since we’re finding where the line crosses the x-axis:\n [ 0 = 2x + 3 ]", "2. Solve for ( x )\n Subtract 3 from both sides:\n [ 2x = -3 ]", "Divide both sides by 2:\n [ x = -\frac{3}{2} ]", "3. Interpret the result\n The x-intercept is the coordinate ( \left( -\frac{3}{2},\ 0 \right) ), meaning the line crosses the x-axis at ( x = -1.5 ).", "### Why is finding the x-intercept important?\n- It helps visualize the line’s position relative to the axes.\n- It’s useful in real-world applications, such as budgeting, physics, and economics, where crossing zero represents no gain, break-even, or equilibrium.\n- Understanding intercepts strengthens your grasp of linear relationships in coordinate geometry.", "In summary, for the line given by ( y = 2x + 3 ), the x-intercept is found by setting ( y = 0 ) and solving — a simple yet powerful technique in algebra.", "Try it yourself! Any line in slope-intercept form allows straightforward calculation of the x-intercept by solving for ( x ) when ( y = 0 ). This foundational skill supports more advanced math and real-life problem solving."]
