Final answer:
The equation of the line passing through the points (-6,6) and (-3,1) is calculated by first determining the slope, which is -5/3, and then using the point-slope form. After rearranging to the slope-intercept form, the final equation of the line is y = (-5/3)x - 4.
Step-by-step explanation:
The student is asking for the equation of a line that passes through the points (-6,6) and (-3,1). To find this equation, we need to calculate the slope (slope) of the line first. The slope is found by the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points. Substituting the values in, we get (1 - 6) / (-3 + 6) = -5 / 3. So, the slope of the line is -5/3. Then, we use the point-slope form of a line, which is y - y1 = m(x - x1), where m is the slope, and (x1, y1) is a point on the line. We can use either of the given points; let's use (-6, 6). The equation of the line is y - 6 = (-5/3)(x + 6).
To find the y-intercept (y-intercept), we can rearrange the equation to the slope-intercept form, y = mx + b. Expanding the current equation gives us y = (-5/3)x - 10 + 6. Simplifying further, we get y = (-5/3)x - 4. Therefore, the equation of the line is y = (-5/3)x - 4.