Final answer:
To find the equation of a line in slope-intercept form that passes through (-4, -3) and (11, 6), calculate the slope (3/5) and then use it to find the y-intercept (-3/5), resulting in the equation y = (3/5)x - (3/5).
Step-by-step explanation:
The question is asking us to find the equation of a line in slope-intercept form, which passes through the points (-4, -3) and (11, 6). To do this, we first need to find the slope (m) of the line. The slope formula is given by m = (y2 - y1) / (x2 - x1). Using the given points (-4, -3) and (11, 6), we find the slope to be:
m = (6 - (-3)) / (11 - (-4)) = 9 / 15 = 3 / 5
Once we have the slope, we can use it along with one of the points to find the y-intercept (b) using the slope-intercept form equation, y = mx + b. Plugging in (-4, -3) and the slope into the equation:
-3 = (3/5)(-4) + b
Which simplifies to:
-3 = -12/5 + b, so b = -3 + 12/5 = -15/5 + 12/5 = -3/5
Therefore, the equation of the line in slope-intercept form is y = (3/5)x - (3/5).