Final answer:
To find the equation of the line in slope-intercept form that passes through (-4, -6) and (0, -9), calculate the slope as -3/4 and use one point to find the y-intercept as -9, resulting in the equation y = -3/4x - 9.
Step-by-step explanation:
To write an equation in slope-intercept form for a line passing through the points (-4, -6) and (0, -9), we firstly need to calculate the slope (m) and then use one of the points to solve for the y-intercept (b). The slope is the change in y divided by the change in x, so the slope m is calculated as follows:
m = (y2 - y1) / (x2 - x1)
m = (-9 - (-6)) / (0 - (-4))
m = (-3) / (4)
m = -3/4
With the slope found, we can now use the y-intercept form of a linear equation, which is y = mx + b. Substituting (0, -9) into this equation for x and y, we can find b:
-9 = (-3/4)(0) + b
-9 = 0 + b
b = -9
Therefore, the equation of the line in slope-intercept form is:
y = -3/4x - 9