the x intercept of a line is -5 and the y intercept of the line is -2. what is the equation of the line
A. y=- 5/2 x-5**
B. y= 2/5 x+2
C. y= 5/2 x-2
D. y= - 2/5 x-2
slope = -2/5
y = -2x/5 + b
0 = -2(-5)/5 + b = 2 + b
b = -2
y = (-2/5) x - 2
Hmm, let me put on my mathematical clown wig and try to solve this for you! 🤡
To find the equation of a line given the x-intercept and y-intercept, we can use the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
Given that the x-intercept is -5, we know that when y equals zero, x equals -5. So, one point on the line is (-5, 0). 📉
Next, let's find the slope (m). We can use the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) is the y-intercept and (x2, y2) is the x-intercept.
Using the points (-5,0) and (0,-2), we can substitute the values into the equation and calculate the slope:
m = (-2 - 0) / (0 - (-5))
m = -2 / 5
m = -2/5
Finally, we have the slope (m = -2/5) and the y-intercept (b = -2). Plugging those values into the slope-intercept form, the equation of the line is:
y = -2/5 x - 2
So, the correct answer is D. y = -2/5 x - 2. Voilà ! 🎉
To find the equation of the line given the x-intercept and y-intercept, we can use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept.
Given that the x-intercept is -5, we know that when y = 0, x = -5, so one point on the line is (-5, 0).
Given that the y-intercept is -2, we know that when x = 0, y = -2, so another point on the line is (0, -2).
Finding the slope (m) of the line:
m = (y2 - y1) / (x2 - x1)
m = (-2 - 0) / (0 - (-5))
m = -2/5
Now we have the slope (m) and the y-intercept (b), which is -2. Therefore, the equation of the line is:
y = (-2/5)x - 2
So the correct option is:
B. y = (2/5)x + 2
To find the equation of a line given its x-intercept and y-intercept, we can use the formula for the equation of a line in slope-intercept form, which is:
y = mx + b
Where m represents the slope of the line and b represents the y-intercept.
In this case, we are given that the x-intercept is -5, which means that the point (-5, 0) lies on the line. We can use this point to find the slope of the line.
Slope (m) = (change in y) / (change in x)
Substituting the coordinates of the x-intercept (-5,0), we have:
Slope (m) = (0 - (-2)) / (-5 - 0)
= 2 / -5
= -2/5
So, the slope of the line is -2/5.
Since we also have the y-intercept as -2, we can substitute the slope (-2/5) and the y-intercept (-2) into the slope-intercept form equation:
y = mx + b
y = -2/5x - 2
Therefore, the equation of the line is y = -2/5x - 2.
So, the correct answer is:
D. y = -2/5x - 2