Question 82·Easy·Linear Equations in Two Variables
In the -plane, the line intersects the -axis at . What is the value of ?
(Express the answer as an integer)
For SAT problems asking where a line intersects an axis, immediately use the fact that on the x-axis, y = 0, and on the y-axis, x = 0. Substitute the appropriate value into the line’s equation and solve the resulting simple equation. This is faster and less error-prone than graphing or doing extra algebra, and it works even when the equation looks more complicated.
Hints
Think about points on the x-axis
What is always true about the -coordinate of any point that lies on the x-axis?
Substitute into the line’s equation
Once you know the -coordinate of a point on the x-axis, plug that value for into the equation .
Solve the resulting equation
After substituting the value for , you will get a simple equation in terms of . Solve this one-step equation to find .
Desmos Guide
Graph the line
In Desmos, type the equation solved for : y = 2x - 10. This is the same line as .
Locate the intersection with the x-axis
On the graph, find where the line crosses the x-axis (where ). Click on that intersection point and note the -coordinate shown; that is the value of in the point .
Step-by-step Explanation
Use the definition of a point on the x-axis
Any point on the x-axis has coordinates , which means its -coordinate is .
So for the intersection point, we know .
Substitute y = 0 into the line’s equation
The line is given by the equation .
Substitute :
This simplifies to:
Solve for x
Solve by dividing both sides by :
So, the value of is 5.