To find the equation of a line given the slope $m = \frac{2}{5}$ and the point $(-10, 1)$, we can use the slope-intercept form of a linear equation, which is:

$y = mx + b$

where:

• $m$ is the slope, and
• $b$ is the y-intercept (the value of $y$ when $x = 0$).

Step 1: Plug in the slope $m = \frac{2}{5}$

$y = \frac{2}{5}x + b$

Step 2: Substitute the point $(-10, 1)$ into the equation to solve for $b$

Substitute $x = -10$ and $y = 1$: $1 = \frac{2}{5}(-10) + b$

Step 3: Simplify and solve for $b$

First, calculate $\frac{2}{5}(-10)$: $\frac{2}{5}(-10) = -4$

Now, substitute back into the equation: $1 = -4 + b$

Solve for $b$: $b = 1 + 4 = 5$

Step 4: Write the final equation of the line

Now that we know $b = 5$, substitute $b$ and $m = \frac{2}{5}$ back into the slope-intercept form: $y = \frac{2}{5}x + 5$

Thus, the equation of the line is: $y = \frac{2}{5}x + 5$

Would you like further explanation, or do you have any questions?

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Here are 5 related questions you could explore:

1. How do you find the equation of a line given two points?
2. What is the significance of the y-intercept in the slope-intercept form?
3. How would the equation change if the slope were negative?
4. How can you rewrite the equation of the line in standard form?
5. What is the graphical interpretation of the slope?

Tip: In slope-intercept form, the slope $m$ tells you how steep the line is, while the intercept $b$ gives you the starting point on the y-axis.