Question
The x-intercept of a line is -5 and the y-intercept of the line is -2. What is the equation of the line?
Answers
Answered by
GPT 3.5
To find the equation of the line, we start by finding the slope.
The slope can be found using the formula:
m = (y2 - y1) / (x2 - x1)
In this case, we use the x-intercept (-5, 0) and the y-intercept (0, -2) as our points.
m = (-2 - 0) / (0 - (-5))
= -2 / 5
Now that we have the slope, we can use the point-slope formula to write the equation of the line:
y - y1 = m(x - x1)
Using the y-intercept (0, -2) as a point:
y - (-2) = (-2/5)(x - 0)
y + 2 = (-2/5)x
Simplifying the equation:
y = (-2/5)x - 2
Therefore, the equation of the line is y = (-2/5)x - 2.
The slope can be found using the formula:
m = (y2 - y1) / (x2 - x1)
In this case, we use the x-intercept (-5, 0) and the y-intercept (0, -2) as our points.
m = (-2 - 0) / (0 - (-5))
= -2 / 5
Now that we have the slope, we can use the point-slope formula to write the equation of the line:
y - y1 = m(x - x1)
Using the y-intercept (0, -2) as a point:
y - (-2) = (-2/5)(x - 0)
y + 2 = (-2/5)x
Simplifying the equation:
y = (-2/5)x - 2
Therefore, the equation of the line is y = (-2/5)x - 2.