Final answer:
To find the equation of a line passing through (-5,4) with a y-intercept of -3, calculate the slope as -7/5, resulting in the line equation y = (-7/5)x - 3.
Step-by-step explanation:
To write an equation of the line that passes through the given point (-5,4) with the given y-intercept of -3, we need to first determine the slope of the line. The slope (m) can be calculated using the change in y-coordinates over the change in x-coordinates between the two points (x1, y1) and (x2, y2), where (-5,4) is (x1, y1) and (0,-3) is (x2, y2), since the y-intercept occurs when x=0.
Using the formula for slope, we get:
m = (y2 - y1) / (x2 - x1)
= (-3 - 4) / (0 - (-5))
= -7 / 5
Now that we have the slope, the equation of the line in slope-intercept form is given by:
y = mx + b
Substituting the slope (m) and y-intercept (b) into the equation:
y = (-7/5)x - 3
So, the equation of the line that passes through (-5,4) with a y-intercept of -3 is y = (-7/5)x - 3.