Questions: Write the equation of the line in fully simplified slope-intercept form.

Transcript text: Write the equation of the line in fully simplified slope-intercept form.

Solution

Solution Steps

Step 1: Find two points on the line.

Two points that are clearly on the line are (-6, -4) and (0, -7).

Step 2: Calculate the slope.

The slope of the line passing through points (x₁, y₁) and (x₂, y₂) is given by: m = (y₂ - y₁) / (x₂ - x₁)

Using the points (-6, -4) and (0, -7): m = (-7 - (-4)) / (0 - (-6)) m = (-7 + 4) / (0 + 6) m = -3 / 6 m = -1/2

Step 3: Use the point-slope form.

The point-slope form of a linear equation is given by: y - y₁ = m(x - x₁)

Using the point (0, -7) and the slope m = -1/2: y - (-7) = -1/2(x - 0) y + 7 = -1/2x

Step 4: Convert to slope-intercept form.

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Subtract 7 from both sides of the equation obtained in Step 3: y = -1/2x - 7

Final Answer

y = -1/2x - 7

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