Question

what is the equation of a line that passes through the points (-3, -5) and (2, 5)? show your work.

part b: what is the slope of the equation above?

part c: what is the y-intercept?

Explanation:

Step1: Find the slope

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1, y_1) = (-3, -5)$ and $(x_2, y_2) = (2, 5)$. Then $m = \frac{5 - (-5)}{2 - (-3)} = \frac{10}{5} = 2$.

Step2: Use point - slope form to find the equation

The point - slope form is $y - y_1 = m(x - x_1)$. Using the point $(2, 5)$ and $m = 2$, we have $y - 5 = 2(x - 2)$.
Simplify: $y - 5 = 2x - 4$, so $y = 2x + 1$.

Part B: Determine the slope

From the equation $y = 2x + 1$ (or from the slope calculation in Step1), the slope $m = 2$.

Part C: Determine the y - intercept

The slope - intercept form is $y = mx + b$, where $b$ is the y - intercept. From $y = 2x + 1$, the y - intercept $b = 1$.

Answer:

• Equation of the line: $y = 2x + 1$
• Slope (Part B): $2$
• y - intercept (Part C): $1$