Final answer:
To determine which lines pass through the given points, the slope of each line is calculated using the coordinates provided. Line 1 is horizontal with an equation of y = -4. Line 2 has a positive slope and Line 3 has a negative slope; their equations can be found using the slope-intercept form.
Step-by-step explanation:
To determine which lines pass through the given points, we need to calculate the slope of the line that would pass through each pair of points and use the coordinates to determine the specific line.
- For the line that goes through the points (-1, -4) and (-4, -4), the slope can be calculated by the formula slope (m) = (y2 - y1) / (x2 - x1). Since the y-coordinates are the same (-4 and -4), the slope is 0, which means the line is horizontal. The equation of the line would be y = -4.
- For the line that goes through the points (-5, 1) and (-1, 4), using the same slope formula, we get slope (m) = (4 - 1) / (-1 + 5) = 3/4. The line has a positive slope, and we can use the slope-intercept form (y = mx + b) to find the equation of the line after finding the intercept.
- Lastly, for the line that goes through points (2, 3) and (3, -2), the slope is calculated as (-2 - 3) / (3 - 2) = -5. This line has a negative slope, and similarly, we can use the slope-intercept form to find the equation of the line.
By examining the slopes and applying the points to the line equation formula, we identify the characteristics and equations of each line