Find the equation to a straight line having slope 1/3 and passing through the point (-2,4)


To find the equation of a straight line with a given slope \( m \) and passing through a specific point, we can use the point-slope form of a line:

\[
y - y_1 = m(x - x_1)
\]

where:
- \( m = \frac{1}{3} \) is the slope,
- \( (x_1, y_1) = (-2, 4) \) is the point the line passes through.

Substitute the given values into the equation:

\[
y - 4 = \frac{1}{3}(x - (-2))
\]
\[
y - 4 = \frac{1}{3}(x + 2)
\]

Now, distribute the \( \frac{1}{3} \):

\[
y - 4 = \frac{1}{3}x + \frac{2}{3}
\]

To simplify further, add 4 to both sides:

\[
y = \frac{1}{3}x + \frac{2}{3} + 4
\]

Convert 4 to a fraction with a denominator of 3:

\[
y = \frac{1}{3}x + \frac{2}{3} + \frac{12}{3}
\]

Now combine the constants:

\[
y = \frac{1}{3}x + \frac{14}{3}
\]

Thus, the equation of the line is:

\[
y = \frac{1}{3}x + \frac{14}{3}
\]

Would you like more details on how the formula works, or have any questions?

Here are 5 related questions you might want to explore:
1. How do you convert from point-slope form to slope-intercept form?
2. What is the general form of a straight line equation?
3. How do you calculate the slope of a line between two points?
4. What happens to the equation of the line if the slope changes?
5. How do you find the x- and y-intercepts of a line?

**Tip:** Always double-check your final answer by plugging the given point into the final equation to ensure consistency.

Find the equation to a straight line having slope 1/3 and passing through the point (-2,4)

Learn how to find the equation of a line with a slope of 1/3 passing through the point (-2, 4) using point-slope and slope-intercept forms. This step-by-step guide covers key algebraic concepts and is ideal for students in Grades 8-10.

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