Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (−2, −4) and (1, −1)

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Identify the two given points: $(-2, -4)$ and $(1, -1)$.

Calculate the slope $m$ using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1) = (-2, -4)$ and $(x_2, y_2) = (1, -1)$.

Use the point-slope form of a line equation: $y - y_1 = m(x - x_1)$, substituting $m$ and one of the points (either $(-2, -4)$ or $(1, -1)$).

Simplify the point-slope form equation if needed, but keep it in the form $y - y_1 = m(x - x_1)$ for the point-slope form answer.

Convert the point-slope form to slope-intercept form $y = mx + b$ by solving for $y$ and simplifying the expression.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Slope of a Line

The slope measures the steepness of a line and is calculated as the change in y-values divided by the change in x-values between two points. For points (x₁, y₁) and (x₂, y₂), slope m = (y₂ - y₁) / (x₂ - x₁). It is essential for writing the equation of a line.

Point-Slope Form of a Line

Point-slope form expresses a line's equation using a known point (x₁, y₁) and the slope m: y - y₁ = m(x - x₁). This form is useful when you know a point on the line and its slope, allowing you to write the equation directly.

Slope-Intercept Form of a Line

Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. After finding the slope and using a point to solve for b, this form clearly shows the line's slope and where it crosses the y-axis.

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