Final answer:
The equation of the line passing through the points (-7, -3) and (-3, 0) is y = 3/4 x + 9/4, which demonstrates it is a line with a positive slope.
Step-by-step explanation:
The question is about finding an equation for a straight line that passes through two given points: (-7, -3) and (-3, 0). To determine the equation, we need to calculate the slope of the line and use the y-intercept or one of the points for the point-slope form. The slope (m) can be found using the formula: m = (y2 - y1) / (x2 - x1).
In this case, the slope will be m = (0 - (-3)) / (-3 - (-7)) = 3 / 4. Given that the slope is positive, the line has a positive slope. Using the slope and one of the points, we can formulate the equation using the point-slope form, which is y - y1 = m(x - x1). Plugging the point (-7, -3) and the slope we have y - (-3) = 3/4 (x - (-7)), or y + 3 = 3/4 (x + 7).
Finally, to get the equation in the slope-intercept form y = mx + b, we simplify to y = 3/4 x + 3/4 * 7 - 3, which simplifies to y = 3/4 x + 21/4 - 12/4, thus y = 3/4 x + 9/4. This is the equation of the line with a positive slope that passes through the points (-7, -3) and (-3, 0).