Questions: Find the equation of the line. Use exact numbers. y= x+

Find the equation of the line. Use exact numbers. y= x+
Transcript text: Find the equation of the line. Use exact numbers. $y=$ $\square$ $x+$ $\square$
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Solution

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Solution Steps

Step 1: Find two points on the line

Two points that are clearly on the line are (0, 3) and (-2, -1).

Step 2: Calculate the slope

The slope, _m_, is given by the formula:

_m_ = (y₂ - y₁) / (x₂ - x₁)

Plugging in our points (0, 3) and (-2, -1), we get:

_m_ = (-1 - 3) / (-2 - 0) _m_ = (-4) / (-2) _m_ = 2

Step 3: Find the y-intercept

The y-intercept is the value of _y_ when _x_ = 0. From the graph, the line crosses the y-axis at y = 3. So, the y-intercept, _b_, is 3.

Step 4: Write the equation in slope-intercept form

The slope-intercept form of a linear equation is: _y_ = _mx_ + _b_, where _m_ is the slope and _b_ is the y-intercept.

Plugging in our values for _m_ and _b_:

_y_ = 2_x_ + 3

Final Answer:

$y = 2x + 3$

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