find the coordinates of the x-intercept oc the line passing through two points (-4,-3) and (2,6) using calculation. then check your answer by graphing it
To find the x-intercept of the line passing through the points (-4,-3) and (2,6), we first need to find the equation of the line in the form y = mx + b, where m is the slope and b is the y-intercept.
First, we find the slope:
m = (y2 - y1) / (x2 - x1)
m = (6 - (-3)) / (2 - (-4))
m = 9 / 6
m = 3/2
Now that we have the slope, we can find the y-intercept using one of the points given (let's use (-4,-3)):
-3 = (3/2)(-4) + b
-3 = -6 + b
b = 3
So the equation of the line passing through the two points is:
y = (3/2)x + 3
To find the x-intercept, we set y = 0 and solve for x:
0 = (3/2)x + 3
-3 = (3/2)x
-6 = 3x
x = -2
Therefore, the x-intercept of the line passing through the points (-4,-3) and (2,6) is (-2, 0).
Now, let's graph the line to verify our answer:
The line passing through the points (-4,-3) and (2,6) is:
y = (3/2)x + 3
Graphing this line shows that it intersects the x-axis at x = -2, confirming our calculated x-intercept.