Question

objectives:

• i can graph a linear equation when in the slope intercept form, $y = mx + b$.
• i can graph a linear equations when in form point slope form, $y - y_1 = m(x - x_1)$.
• i can graph a linear equation when in standard form, $ax + by = c$.
• i can determine the slope when given two points.
• i can determine if the graph is proportional or not.
• i can determine if lines are parallel or perpendicular.

practice problems.

1. find the slope which goes through the points (3,7) and (-1, 5).

slope=__________

1. find the slope which goes through the points (2,-9) and (21, 5).

slope=__________

Explanation:

Step1: Recall the slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Solve problem 16

For points \( (3,7) \) and \( (-1,5) \), let \( (x_1, y_1)=(3,7) \) and \( (x_2, y_2)=(-1,5) \).
Substitute into the slope formula: \( m=\frac{5 - 7}{-1 - 3}=\frac{-2}{-4}=\frac{1}{2} \).

Step3: Solve problem 17

For points \( (2,-9) \) and \( (21,5) \), let \( (x_1, y_1)=(2,-9) \) and \( (x_2, y_2)=(21,5) \).
Substitute into the slope formula: \( m=\frac{5 - (-9)}{21 - 2}=\frac{14}{19} \).

Answer:

1. Slope = \(\frac{1}{2}\)
2. Slope = \(\frac{14}{19}\)