Final answer:
To find the slope-intercept form of the line through (-4,2) and (-3,-4), calculate the slope (m=-6) and use one point to find the y-intercept (b=-18), resulting in the equation y = -6x - 18.
Step-by-step explanation:
To find the slope-intercept equation of the line passing through the points (-4,2) and (-3,-4), you must first calculate the slope (m) by using the points:
m = (Y2 - Y1) / (X2 - X1)
m = (-4 - 2) / (-3 + 4)
m = -6 / 1
m = -6
Now that we have the slope, we can utilize one of the points to find the y-intercept (b). Assuming we choose the point (-4,2), the equation becomes:
y - y1 = m(x - x1)
2 - (-4) = -6(-4 - x)
2 + 4 = -6(-4) + 6x
6 = 24 + 6x
6 - 24 = 6x
-18 = 6x
x = -3
Therefore, the slope-intercept form of the equation is y = -6x - 18.
An important aspect of linear equations is that the slope is constant along a straight line. In various examples stated, lines with the same slope display how the initial values determine the overall position of the line, while the slope determines its inclination.