Answer:
To find the equation of a line that intersects the points (6 -4) and (7 4 we can use the slope-intercept form of a linear equation which is y = mx + b.
First let's find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (6 -4) and (7 4 we have:
m = (4 - (-4)) / (7 - 6)
m = 8/1
m = 8
Now that we have the slope we can proceed to find the y-intercept (b). We can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Using the point (6 -4) and the slope (m = 8 we have:
y - (-4) = 8(x - 6)
y + 4 = 8(x - 6)
y + 4 = 8x - 48
Now let's simplify the equation:
y = 8x - 52
Therefore the equation of the line that intersects the points (6 -4) and (7 4) is y = 8x - 52.