How to find y intercept with a point and slope?
Understand the Problem
The question is asking how to determine the y-intercept of a linear equation given a specific point and the slope of the line. To find the y-intercept, we can use the point-slope form of a linear equation and rearrange it to find where the line crosses the y-axis.
Answer
The y-intercept is $-5$.
Answer for screen readers
The y-intercept is $-5$.
Steps to Solve
- Identify the given values
From the problem, we have a point $(x_1, y_1)$ and the slope $m$. For example, suppose the point is $(2, 3)$ and the slope is $4$. Here, $x_1 = 2$, $y_1 = 3$, and $m = 4$.
- Write the point-slope form of the equation
The point-slope form of a linear equation is given by:
$$ y - y_1 = m(x - x_1) $$
Substituting the known values into the equation gives:
$$ y - 3 = 4(x - 2) $$
- Distribute the slope
Now we distribute $m$ across the terms in the parentheses:
$$ y - 3 = 4x - 8 $$
- Rearrange to solve for $y$
Next, we add $3$ to both sides to isolate $y$:
$$ y = 4x - 5 $$
- Identify the y-intercept
The y-intercept is the value of $y$ when $x = 0$. Substitute $0$ for $x$ in the equation:
$$ y = 4(0) - 5 = -5 $$
Therefore, the y-intercept is $-5$.
The y-intercept is $-5$.
More Information
The y-intercept of a linear equation is important because it tells us where the line crosses the y-axis. In graphical terms, it represents the value of $y$ when $x$ is zero. Knowing just one point and the slope allows us to fully define the line.
Tips
- Not properly substituting the values into the equation.
- Forgetting to simplify before identifying the y-intercept.
- Not understanding that the y-intercept occurs when $x=0$.
