Answer:To write the equation of a line that passes through the given points (0, -5) and (-10, -21), we can use the point-slope form of a linear equation.
1) Start with the point-slope form of a linear equation:
y - y1 = m(x - x1)
where (x1, y1) represents one of the given points and m represents the slope.
2) Choose one of the points and substitute its coordinates into the equation. Let's use the point (0, -5):
y - (-5) = m(x - 0)
3) Simplify the equation:
y + 5 = mx
4) Determine the slope (m) using the two given points. The slope is calculated as the change in y divided by the change in x:
m = (change in y) / (change in x)
m = (-21 - (-5)) / (-10 - 0) = -16 / -10 = 8 / 5
5) Substitute the slope into the equation:
y + 5 = (8/5)x
6) To convert the equation to slope-intercept form, isolate y by subtracting 5 from both sides of the equation:
y = (8/5)x - 5
Therefore, the equation of the line that passes through the points (0, -5) and (-10, -21) is y = (8/5)x - 5.
Explanation: