-What is the equation of the line that passes through the point (-2,-7) and has a slope of 6? Answer Attemptiout of 2 square

To find the equation of a line that passes through a given point and has a specific slope, we can use the point-slope form of a linear equation. The point-slope form is given by:<br /><br />\[ y - y_1 = m(x - x_1) \]<br /><br />where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope of the line.<br /><br />Given:<br />- Point: \( (-2, -7) \)<br />- Slope: \( 6 \)<br /><br />Substitute these values into the point-slope form:<br /><br />\[ y - (-7) = 6(x - (-2)) \]<br /><br />Simplify the equation:<br /><br />\[ y + 7 = 6(x + 2) \]<br /><br />Distribute the 6 on the right side:<br /><br />\[ y + 7 = 6x + 12 \]<br /><br />Subtract 7 from both sides to isolate \( y \):<br /><br />\[ y = 6x + 12 - 7 \]<br /><br />\[ y = 6x + 5 \]<br /><br />So, the equation of the line is:<br /><br />\[ y = 6x + 5 \]