What is the equation of the line that passes through the point left bracket, minus, 3, comma, minus, 8, right bracket(−3,−8) and has a slope of 4?
Answer
To find the equation of the line that passes through a given point (-3, -8) with a slope of 4, we can use the point-slope form of the line equation:
\[ y - y_1 = m(x - x_1) \]
Here, \(m\) is the slope of the line, and \((x_1, y_1)\) is the point through which the line passes. In this case, \(m = 4\), \(x_1 = -3\), and \(y_1 = -8\). Plugging these values into the equation, we get:
\[ y - (-8) = 4(x - (-3)) \]
Simplifying further by distributing and moving terms around:
\[ y + 8 = 4(x + 3) \]
\[ y + 8 = 4x + 12 \]
Subtracting 8 from both sides to solve for y, we have:
\[ y = 4x + 12 - 8 \]
\[ y = 4x + 4 \]
So, the equation of the line in slope-intercept form (y = mx + b) is:
\[ y = 4x + 4 \]