Question

given the slope $\frac{-3}{4}$ and the initial point (1,-3), what would be another point on the line?
(-5, 6)
(5, -6)
(-6, 5)
(6, 5)

Explanation:

Step1: Recall the slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \( m = -\frac{3}{4} \), \( (x_1, y_1)=(1, - 3) \), and we check each option \( (x_2, y_2) \).

Step2: Check option (5, -6)

Substitute \( (x_1, y_1)=(1, - 3) \) and \( (x_2, y_2)=(5, - 6) \) into the slope formula:
\( m=\frac{-6-(-3)}{5 - 1}=\frac{-6 + 3}{4}=\frac{-3}{4} \), which matches the given slope.

Step3: Verify other options (optional but for completeness)

• For \( (-5,6) \): \( m=\frac{6-(-3)}{-5 - 1}=\frac{9}{-6}=-\frac{3}{2}

eq-\frac{3}{4} \)

• For \( (-6,5) \): \( m=\frac{5-(-3)}{-6 - 1}=\frac{8}{-7}

eq-\frac{3}{4} \)

• For \( (6,5) \): \( m=\frac{5-(-3)}{6 - 1}=\frac{8}{5}

eq-\frac{3}{4} \)

Answer:

B. (5, -6)