The equation of line s is y=
–
4x–
5
3
. Line t includes the point (
–
3,3) and is parallel to line s. What is the equation of line t?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.


The given equation of line \( s \) is:

\[
y = -\frac{4}{3}x - \frac{5}{3}
\]

We are told that line \( t \) is parallel to line \( s \), which means that the slopes of both lines are the same. The slope of line \( s \) is \( -\frac{4}{3} \), so the slope of line \( t \) is also \( -\frac{4}{3} \).

Now, we are given that line \( t \) passes through the point \( (-3, 3) \). To find the equation of line \( t \), we can use the point-slope form of the equation of a line, which is:

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

where \( m \) is the slope, and \( (x_1, y_1) \) is the point the line passes through. Substituting the known values:

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

Now, we will simplify this equation step by step:

1. Distribute the slope \( -\frac{4}{3} \) on the right-hand side:

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

2. Add 3 to both sides to isolate \( y \):

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

3. Simplify the constants:

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

Thus, the equation of line \( t \) in slope-intercept form is:

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

Would you like more details or have any questions?

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Here are 5 related questions to expand on this concept:
1. How would you find the equation of a line perpendicular to line \( s \)?
2. How does the slope of a line relate to its steepness and direction?
3. Can you explain how to derive the slope-intercept form from the general equation of a line?
4. What is the significance of parallel and perpendicular lines in geometry?
5. How would you graph the lines \( s \) and \( t \) on a coordinate plane?

**Tip:** When two lines are parallel, their slopes are always equal.

Line t includes the point (-3, 3) and is parallel to line s with the equation y = -4/3x - 5/3. What is the equation of line t? Write the equation in slope-intercept form.

Learn how to find the equation of a line parallel to y = -4/3x - 5/3 that passes through the point (-3, 3). This problem involves key concepts like slope-intercept form and the relationship between parallel lines. Suitable for students in Grades 8-10.

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