Write the point-slope form of the equation of the line...

Write the point-slope form of the equation of the line satisfying each of the conditions. Then use the point-slope form to write the slope-intercept form of the equation in function notation.
Passing through $(-2,-5)$ and $(3,-5)$

Key Concepts

Slope

The slope of a line represents its steepness and direction, calculated by the change in the vertical direction divided by the change in the horizontal direction between two points on the line. It is typically computed with the formula m = (y? - y?)/(x? - x?), allowing one to quantify how much y increases or decreases for each unit increase in x.

Point-Slope Form

The point-slope form of a linear equation is used to express the equation of a line when a point on the line and its slope are known. It is given by the formula y - y? = m(x - x?), where (x?, y?) is a specific point on the line and m is its slope. This form is particularly useful in formulating the equation of a line directly from a known point and slope.

Slope-Intercept Form

The slope-intercept form of a line is one of the most common representations of a linear equation. It is expressed as y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis. This form is advantageous for quickly identifying the slope and intercept of a line.

Function Notation

Function notation is a way of writing functions that emphasize the dependent relationship between input and output, typically using f(x) to denote the output corresponding to the input x. When a linear equation is rewritten using function notation (e.g., f(x) = mx + b), it clearly indicates that it represents a function where every x-value has a corresponding y-value.

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