The straight line L has equation 2y + 7x = 10. Find the coordinates of the point where L crosses the y-axis.
Understand the Problem
The question asks to find the y-intercept of the equation 2y + 7x = 10. To do this, we set x=0 and solve for y.
Answer
$(0, 5)$
Answer for screen readers
$(0, 5)$
Steps to Solve
- Substitute $x = 0$ into the equation
To find the y-intercept, we set $x = 0$ in the given equation $2y + 7x = 10$. $2y + 7(0) = 10$
- Simplify the equation
Simplify the equation by performing the multiplication. $2y + 0 = 10$ $2y = 10$
- Solve for $y$
Divide both sides of the equation by 2 to isolate $y$. $\frac{2y}{2} = \frac{10}{2}$ $y = 5$
- Express the y-intercept as coordinates
The y-intercept is the point where the line crosses the y-axis, which occurs when $x=0$ and $y=5$. Therefore, the coordinates are $(0, 5)$.
$(0, 5)$
More Information
The y-intercept is the point on the y-axis where a line intersects it. It's always in the form of $(0, y)$.
Tips
A common mistake is to set $y = 0$ instead of $x = 0$ when finding the y-intercept. Remember that the y-intercept occurs where the line crosses the y-axis, which means the x-coordinate is 0. Also, remember to express the answer as coordinates $(x, y)$ and not just the $y$ value.
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