Final answer:
The standard form of the line passing through (-4, -5) and (1, -1) is -4x + 5y = -9. The x-intercept is 9/4 or 2.25, and the y-intercept is -9/5 or -1.8.
Step-by-step explanation:
To find an equation of a line in standard form passing through two points, we need to start by calculating the slope of the line. The slope m is determined by the change in y divided by the change in x between two points (x1, y1) and (x2, y2).
In this case, we have the points (-4, -5) and (1, -1). So the slope m is calculated as:
m = (y2 - y1) / (x2 - x1)
m = (-1 - (-5)) / (1 - (-4))
m = (4) / (5)
m = 4/5
The slope is positive, so we know it's not a line with a negative slope. We can use the slope and one point to write the slope-intercept form of the line: y - y1 = m(x - x1). Using the point (-4, -5), we get:
y + 5 = (4/5)(x + 4)
To convert this to standard form (Ax + By = C), we clear the fractions and move all terms involving variables to the left side and constant terms to the right side of the equation:
5(y + 5) = 4(x + 4)
5y + 25 = 4x + 16
-4x + 5y = -9
The standard form of the line is -4x + 5y = -9. Now, to find the x-intercept, set y to 0 and solve for x:
-4x = -9
x = 9/4
The x-intercept is 9/4 or 2.25.
To find the y-intercept, set x to 0 and solve for y:
5y = -9
y = -9/5
The y-intercept is -9/5 or -1.8.