Choose the equation in slope-intercept form for the line passing through each pair of points (1/2, 1) and 1, 5)
y=1/8x+39/8
y=1/2x+9/2
y=2x+3
y=8x-3 (*)
To find the equation of a line in slope-intercept form (y = mx + b), you need to determine the values of slope (m) and y-intercept (b).
Given the points (1/2, 1) and (1, 5), we can use the slope formula to find the slope (m):
m = (y2 - y1) / (x2 - x1)
Substituting the values, we get:
m = (5 - 1) / (1 - 1/2)
m = 4 / (1/2)
m = 4 * 2
m = 8
Next, we can choose any of the given equations and substitute the slope value (8) into the equation. Let's check option D:
y = 8x - 3
Now, substitute the coordinates of one of the given points into the equation to find the y-intercept (b). Let's use (1/2, 1):
1 = 8(1/2) - 3
1 = 4 - 3
1 = 1
Since both sides of the equation are equal, the point (1/2, 1) lies on the line.
Therefore, the equation y = 8x - 3 is the equation in slope-intercept form for the line passing through the points (1/2, 1) and (1, 5).