Final answer:
To find the equation of a line passing through (-4,-4) with a slope of -3/4, you start with the point-slope form and then simplify to get the slope-intercept form, resulting in the equation y = -3/4x - 7.
Step-by-step explanation:
To write an equation that passes through the point (-4,-4) and has a slope of -3/4, you can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. Plugging in our point and slope, we get:
y - (-4) = -3/4(x - (-4))
Simplify this equation by distributing the slope and adding 4 to both sides:
y + 4 = -3/4x - 3
Finally, subtract 4 from both sides to get the equation in slope-intercept form:
y = -3/4x - 7
Now, the equation y = -3/4x - 7 represents the line that passes through the point (-4,-4) with a slope of -3/4.