Question

the equation of line s is $y = -4x - \frac{5}{3}$. 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.

Explanation:

Step1: Identify parallel line slope

Parallel lines have equal slopes. For line \(s: y = -4x - \frac{5}{3}\), the slope \(m = -4\), so line \(t\) also has \(m = -4\).

Step2: Substitute point into slope-intercept form

Slope-intercept form is \(y = mx + b\). Substitute \(x = -3\), \(y = 3\), \(m = -4\):
\(3 = -4(-3) + b\)

Step3: Solve for y-intercept \(b\)

Calculate \( -4(-3) = 12 \), so:
\(3 = 12 + b\)
\(b = 3 - 12 = -9\)

Step4: Write line t's equation

Substitute \(m = -4\) and \(b = -9\) into \(y = mx + b\).

Answer:

\(y = -4x - 9\)