would the equation in slope-intercept form of the line which passes through 0,6 and 4,3 be y = -3/4x + 6?
correct. Online, it's best to leave a space after fractions, so it doesn't look like 3/(4x)
3/4 x is better
or (3/4)x
Thanks, I'll keep that in mind.
To determine whether the equation you provided, y = -3/4x + 6, represents the line passing through the points (0, 6) and (4, 3), we can follow a simple process to check.
1. Begin by calculating the slope of the line using the two given points.
Slope (m) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (0, 6) and (4, 3), the slope can be calculated as follows:
m = (3 - 6) / (4 - 0)
m = -3 / 4
2. Verify whether the slope matches the value in the equation you provided.
Comparing the calculated slope (-3/4) with the slope in the equation (-3/4x), we confirm that they match.
3. Finally, substitute one of the given points into the equation and check whether the equation holds true.
Using the point (4, 3):
y = -3/4x + 6
3 = -3/4(4) + 6
3 = -12/4 + 6
3 = -3 + 6
3 = 3
Since the equation holds true for the given point, we can conclude that the equation y = -3/4x + 6 represents the line passing through the points (0, 6) and (4, 3).