Given that line $s$ has the equation:

$y = -10x + \frac{5}{4}$

The slope of line $s$ is $m = -10$, since the equation is in the slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Since line $t$ is parallel to line $s$, it will have the same slope, $m = -10$. Line $t$ passes through the point $(-1, 3)$.

We can use the point-slope form of the equation of a line to find the equation of line $t$. The point-slope form is:

$y - y_1 = m(x - x_1)$

Where $m$ is the slope, and $(x_1, y_1)$ is a point on the line. Plugging in the known values:

• $m = -10$
• $(x_1, y_1) = (-1, 3)$

Substitute these values into the point-slope form:

$y - 3 = -10(x - (-1))$

Simplify:

$y - 3 = -10(x + 1)$

Now distribute the $-10$:

$y - 3 = -10x - 10$

Finally, add 3 to both sides to solve for $y$:

$y = -10x - 7$

Thus, the equation of line $t$ is:

$y = -10x - 7$

Let me know if you'd like more explanation or further questions!

Here are 5 related questions:

1. How do you convert between point-slope form and slope-intercept form?
2. What does the slope of a line represent geometrically?
3. How can you determine if two lines are parallel or perpendicular?
4. What is the relationship between parallel lines in terms of slope?
5. How do you write the equation of a line given two points on it?

Tip: Remember that parallel lines have identical slopes, and they never intersect.