The x-intercept of the graph y = 4x − 36 is (9, 0).
How do you find the x-intercept of a line?
Set y = 0 and solve for x in the equation.
Picture the x-intercept as where the line kisses the x-axis—flat against it, with zero height. (That’s why y has to be zero.) Plug in 0 for y, then solve for x. Same trick works for y-intercepts: freeze x at zero and solve for y. I still think of it as “pausing” one axis so the other one spills out its exact coordinate. If you're working with more complex equations, you might need to explore the equation of a line to understand intercepts better.
What is the x-intercept of y = 4x − 36?
The x-intercept is (9, 0).
Rewrite the equation to y = 4x − 36. Next, set y to 0: 0 = 4x − 36. Add 36 to both sides (4x = 36) and divide by 4. That gives x = 9, so the intercept is the point (9, 0).
What are the x- and y-intercepts of y = 4x?
The x-intercept is undefined; the y-intercept is (0, 0).
If the equation is simply y = 4x, setting y = 0 gives 0 = 4x ⇒ x = 0. That means the only intercept is the origin. The line slices right through (0, 0), so there’s no separate x-intercept to speak of. This concept of intercepts is also relevant in understanding geographic spread in data visualization.
What is the x-intercept of y = −2x + 4?
The x-intercept is (2, 0).
Assume the equation is y = −2x + 4. Set y = 0: 0 = −2x + 4. Move the −2x to the other side (2x = 4) and divide by 2. You’ll get x = 2, so the intercept is (2, 0).
What is the slope of 4x + 9y = 36?
Rewrite 4x + 9y = 36 into slope-intercept form. Subtract 4x from both sides (9y = −4x + 36) and divide by 9. That gives y = (−4/9)x + 4. The number in front of x is the slope, so m = −4/9.
How do you rewrite 3x + 4y = 8?
Rearrange to y = (3/4)x + 2.
Start with 3x + 4y = 8. Subtract 3x from both sides (4y = −3x + 8) and divide everything by 4. You end up with y = (3/4)x + 2, ready for graphing or whatever you need next.
What’s the quickest way to find an x-intercept?
Set y = 0 and solve for x in the equation.
There’s no magic formula—just the standard move. For any line y = mx + b, drop y to zero and solve. If the equation is in standard form Ax + By = C, the x-intercept is simply C/A. That’s all there is to it. Understanding this process can help in analyzing effective paragraph structures in mathematical writing.
What exactly is an x-intercept?
An x-intercept is the point where a graph crosses the x-axis (y = 0).
Think of the x-axis as the floor. The intercept is the exact spot where the line touches that floor. Each intercept is an (x, 0) pair. A horizontal line floating above or below the floor never touches it, so it has zero x-intercepts.
What does “x-intercept” actually mean?
The x-intercept is the x-value where a curve meets the x-axis.
At that exact spot, the y-value is zero. Graphically, it’s the number you read on the x-axis when the line or curve lands on it. Algebraically, it’s the solution you get when you set y = 0 and solve for x.
What is the x-intercept of y = 3x?
The x-intercept is (0, 0).
For y = 3x, set y = 0: 0 = 3x ⇒ x = 0. The line runs straight through the origin, so both intercepts land on the same point (0, 0).
Can an x-intercept be missing?
Yes; horizontal lines not on the x-axis have no x-intercept.
Any line y = k where k isn’t zero never meets the x-axis, so it has zero x-intercepts. Vertical lines x = k always hit the x-axis at (k, 0), giving exactly one x-intercept. This principle is similar to how repairing hardware requires precise alignment to function correctly.
What are the intercepts of 4x + 3y = −12?
The x-intercept is (−3, 0); the y-intercept is (0, 4).
For the x-intercept, set y = 0: 4x = −12 ⇒ x = −3. For the y-intercept, set x = 0: 3y = −12 ⇒ y = −4? Wait, no—let me double-check that last step. Actually, −3y = −12 ⇒ y = 4. Plot both points to sketch the line fast.
What’s the slope of y = −2x + 4?
Written as y = −2x + 4, the number in front of x is the slope. This line drops 2 units for every 1 unit it moves to the right—pretty steep downward.
Is y = 2x + 4 a linear equation?
Yes, it is a linear equation.
A linear equation always graphs as a straight line. Any equation that can be written y = mx + b (or tweaked versions) counts, and y = 2x + 4 fits perfectly.
What is the y-intercept of y = 2x?
The y-intercept is (0, 0).
The equation y = 2x runs straight through the origin. When x = 0, y = 0, so the y-intercept is the point (0, 0).
