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Difficulty: EasyLinear Equations and Graphing

In the standard (x,y)(x, y) coordinate plane, the line defined by the equation 3x−4y=243x - 4y = 24 intersects the xx-axis at a certain point. What is the xx-coordinate of this intersection point?

Answer: 8

Answer

The xx-coordinate of the intersection point is 88.
To find the xx-intercept, set y=0y = 0 in the equation 3x−4y=243x - 4y = 24. This simplifies to 3x=243x = 24. Dividing both sides of the equation by 33 gives x=8x = 8.

Step-by-Step Solution

1
Set y=0y = 0 in the equation.
3x−4(0)=24  ⟹  3x=243x - 4(0) = 24 \implies 3x = 24
The intersection of any graph with the xx-axis occurs where the yy-coordinate is 00.
2
Solve for xx.
x=8x = 8
Dividing both sides of 3x=243x = 24 by 33 isolates the variable xx.

Key Concept

Finding the xx-intercept of a line by setting y=0y = 0

Alternative Method

Convert the standard form equation 3x−4y=243x - 4y = 24 into slope-intercept form: −4y=−3x+24  ⟹  y=34x−6-4y = -3x + 24 \implies y = \frac{3}{4}x - 6. To find the xx-intercept, set y=0y = 0 and solve the equation 0=34x−6  ⟹  6=34x  ⟹  x=80 = \frac{3}{4}x - 6 \implies 6 = \frac{3}{4}x \implies x = 8.
Estimated Time:45s
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Topics

Linear Equations and Graphing

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