Question 6, 2.3.57
HW Score: $33.33 \%$,
Points: 0 of 1
Find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line.
Containing the points $(-3,-6)$ and $(-1,-7)$

The equation is $\square$.
(Type an equation. Simplify your answer.)

Step 1 ：Find the slope (m) using the formula \(m = \frac{{y2 - y1}}{{x2 - x1}}\). Substitute the given points (-3,-6) and (-1,-7) into the formula to get \(m = \frac{{-7 - (-6)}}{{-1 - (-3)}} = -0.5\).

Step 2 ：Find the y-intercept (b) using the slope-intercept form of the line, \(y = mx + b\), and one of the given points (-3,-6). Substitute the values into the equation to get \(-6 = -0.5*(-3) + b\), which simplifies to \(b = -6 - 1.5 = -7.5\).

Step 3 ：Write the equation of the line using the slope and y-intercept. The equation of the line in slope-intercept form is \(y = -0.5x - 7.5\).

Step 4 ：Check the solution by substituting the coordinates of the two points into the equation. For (-3,-6), \(y = -0.5*(-3) - 7.5 = -6\). For (-1,-7), \(y = -0.5*(-1) - 7.5 = -7\). Both points satisfy the equation, so the solution is correct.

Step 5 ：\(\boxed{y = -0.5x - 7.5}\) is the equation of the line that passes through the points (-3,-6) and (-1,-7).