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X Intercept: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">X InterceptX Intercept: Definition and ExamplesTable of ContentsX-Intercept: Definition, Formula, and Examples Definition of X-Intercept

The x-intercept is a point where the graph of a function or curve intersects with the x-axis in the coordinate system. On the Cartesian plane, it represents the value of the x-coordinate at a point where the y-coordinate equals zero. X-intercepts are also known as "horizontal intercepts," "roots," "zeros," or "solutions" of the function.

A function may have one, zero, or many x-intercepts depending on how many times it crosses the x-axis. To find the x-intercept of any equation, we substitute y=0y = 0y=0 into the equation and solve for xxx. This works for different forms of linear equations (general form, slope-intercept form, point-slope form, and intercept form) as well as for quadratic equations using the quadratic formula.

Examples of X-Intercept Example 1: Finding the X-Intercept of a Linear Equation Problem:

Find the x-intercept of the line 5x−6y+15=05x - 6y + 15 = 05x−6y+15=0.

Step-by-step solution:

Step 1, Remember that the x-intercept is found when y = 0. Let's substitute y=0y = 0y=0 into our equation. 5x−6(0)+15=05x - 6(0) + 15 = 05x−6(0)+15=0

Step 2, Simplify the equation after substituting. 5x+15=05x + 15 = 05x+15=0

Step 3, Isolate x to find the x-intercept.

5x=−155x = -155x=−15 x=−3x = -3x=−3

Step 4, Check the answer. The x-intercept is at the point (−3,0)(-3,0)(−3,0).

Example 2: Finding the X-Intercepts of a Quadratic Equation Problem:

What is the x-intercept of the quadratic equation given by: 2x2+7x−9=02x^2 + 7x - 9 = 02x2+7x−9=0?

Step-by-step solution:

Step 1, For a quadratic equation in the form ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0, we can find the x-intercepts using the quadratic formula: x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}x=2a−b±b2−4ac​​

Step 2, Identify the values of aaa, bbb, and ccc in our equation. a=2,b=7,c=−9a = 2, b = 7, c = -9a=2,b=7,c=−9

Step 3, Substitute these values into the quadratic formula.

x=−7±72−4×2×(−9)2×2x = \frac{-7 \pm \sqrt{7^2 - 4 \times 2 \times (-9)}}{2 \times 2}x=2×2−7±72−4×2×(−9)​​ x=−7±49+724x = \frac{-7 \pm \sqrt{49 + 72}}{4}x=4−7±49+72​​

Step 4, Simplify the expression under the square root.

x=−7±1214x = \frac{-7 \pm \sqrt{121}}{4}x=4−7±121​​ x=−7±114x = \frac{-7 \pm 11}{4}x=4−7±11​

Step 5, Find both x-intercept values.

x=−7−114=−184=−92=−4.5x = \frac{-7 - 11}{4} = \frac{-18}{4} = -\frac{9}{2} = -4.5x=4−7−11​=4−18​=−29​=−4.5 x=−7+114=44=1x = \frac{-7 + 11}{4} = \frac{4}{4} = 1x=4−7+11​=44​=1

Step 6, The x-intercepts are at (−4.5,0)(-4.5, 0)(−4.5,0) and (1,0)(1, 0)(1,0), meaning this parabola crosses the x-axis at two points.

Example 3: Finding the Equation of a Line Using X-Intercept and Slope Problem:

Find the equation of a line if slope = 6 and the x-intercept = 7.

Step-by-step solution:

Step 1, Start with the slope-intercept form of a line: y=mx+cy = mx + cy=mx+c, where m is the slope and ccc is the y-intercept.

Step 2, Use the formula that relates x-intercept to slope and y-intercept. If the x-intercept is at x=ax = ax=a, then:

a=−cma = \frac{-c}{m}a=m−c​

Step 3, Substitute the known values: slope m=6m = 6m=6 and x-intercept = 7.

7=−c67 = \frac{-c}{6}7=6−c​

Step 4, Solve for ccc (the y-intercept).

7×6=−c7 \times 6 = -c7×6=−c 42=−c42 = -c42=−c c=−42c = -42c=−42

Step 5, Write the final equation of the line by substituting mmm and ccc into the slope-intercept form. y=6x−42y = 6x - 42y=6x−42

Comments(2)HHostEveNovember 4, 2025I've used this x-intercept def for my students. It's super clear, and the examples really helped them grasp the concept. Thanks!

NNatureLover85September 17, 2025This explanation of x-intercepts was super clear and the examples really helped my son understand his math homework. We’ve bookmarked the page for future study sessions!

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