Final answer:
The equation of the line passing through the points (5,1.9) and (4,1.7) is found by first calculating the slope (0.2) and then using the point-slope formula to determine the y-intercept (0.9). Thus, the equation in slope-intercept form is y = 0.2x + 0.9, which is option a.
Step-by-step explanation:
To find the equation of the line in slope-intercept form that passes through the points (5,1.9) and (4,1.7), you first calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
For our points, (x1, y1) = (5, 1.9) and (x2, y2) = (4, 1.7), we get:
m = (1.7 - 1.9) / (4 - 5)
Which simplifies to:
m = (-0.2) / (-1)
Therefore, the slope m is:
m = 0.2
Next, we use the point-slope form to find the y-intercept (b):
y - y1 = m(x - x1)
Plugging in the slope and either point, for instance, (5, 1.9):
1.9 - b = 0.2(5 - x)
Now we solve for b:
b = 1.9 - (0.2 × 5)
which results in:
b = 0.9
Hence, the equation in slope-intercept form is:
y = 0.2x + 0.9
The correct answer is option a. y = 0.2x + 0.9.