A line has equation $3y = 3x - 2$. Circle the coordinates of the intercept of the line with the y-axis.
Understand the Problem
The question provides the equation of a line, $3y = 3x - 2$, and asks to identify the coordinates of the y-intercept. The y-intercept is the point where the line crosses the y-axis, which occurs when $x = 0$. To find the y-coordinate of the y-intercept, substitute $x = 0$ into the equation and solve for $y$.
Answer
$(0, -\frac{2}{3})$
Answer for screen readers
$(0, -\frac{2}{3})$
Steps to Solve
- Substitute $x=0$ into the equation
To find the y-intercept, we set $x = 0$ in the equation $3y = 3x - 2$. $$3y = 3(0) - 2$$
- Simplify the equation
Simplifying the equation gives: $$3y = -2$$
- Solve for $y$
Divide both sides of the equation by 3: $$y = -\frac{2}{3}$$
- Write the coordinates
The y-intercept is the point where $x = 0$ and $y = -\frac{2}{3}$. Therefore, the coordinates are $(0, -\frac{2}{3})$.
$(0, -\frac{2}{3})$
More Information
The y-intercept is where a line crosses the y-axis. It can be visually identified on any graph of a line, and the equation of a line can be written in slope-intercept form which makes it easy to identify.
Tips
A common mistake is to forget to divide by 3 when solving for $y$. Another mistake is to mix up the $x$ and $y$ coordinates or to forget that the x-coordinate of the y-intercept is always 0.
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