Find the x- and y-intercepts of the line that passes through the given points.
(-6,-6), (4,-2)
First, let's find the slope of the line using the formula:
\(m = \frac{{y_2-y_1}}{{x_2-x_1}}\)
Using the points (-6,-6) and (4,-2):
\(m = \frac{{(-2)-(-6)}}{{4-(-6)}} = \frac{{4}}{{10}} = \frac{{2}}{{5}}\)
Now, let's find the y-intercept (b) using the formula of a line:
\(y = mx + b\)
Substituting one of the points (-6,-6) and the slope \(\frac{{2}}{{5}}\):
\(-6 = \frac{{2}}{{5}}(-6) + b\)
Simplifying:
\(-6 = -\frac{{12}}{{5}} + b\)
Multiplying both sides by 5:
\(-30 = -12 + 5b\)
Adding 12 to both sides:
\(-18 = 5b\)
Dividing both sides by 5:
\(b = -\frac{{18}}{{5}}\)
So, the y-intercept is \(-\frac{{18}}{{5}}\).
Now, let's find the x-intercept. The x-intercept is the point on the line where y=0. We can substitute this into the equation of the line and solve for x:
\(0 = \frac{{2}}{{5}}x -\frac{{18}}{{5}}\)
Adding \(\frac{{18}}{{5}}\) to both sides:
\(\frac{{18}}{{5}} = \frac{{2}}{{5}}x\)
Multiplying both sides by \(\frac{{5}}{{2}}\):
\(9 = x\)
So, the x-intercept is 9.
Therefore, the x-intercept is 9 and the y-intercept is \(-\frac{{18}}{{5}}\).