Final answer:
The equation in slope-intercept form for the line passing through the points (4.2, 3.6) and (1.8, -1.2) is y = 2x - 4.8, obtained by first calculating the slope (2) and then using the point-slope form to find the y-intercept (-4.8).
Step-by-step explanation:
To find an equation in slope-intercept form for the line that passes through the points (4.2, 3.6) and (1.8, -1.2), we first need to determine the slope of the line. The slope (m) is calculated as the change in y divided by the change in x, which from the points provided is:
m = (y2 - y1) / (x2 - x1) = (3.6 - (-1.2)) / (4.2 - 1.8) = 4.8 / 2.4 = 2.
Now that we have the slope, we can use point-slope form to create the equation of the line. Choosing one of the points, for example, (4.2, 3.6), we have:
y - y1 = m(x - x1)
y - 3.6 = 2(x - 4.2)
Expanding this and solving for y to put it into slope-intercept form (y = mx + b), we get:
y = 2x - 8.4 + 3.6
y = 2x - 4.8
Therefore, the equation of the line in slope-intercept form is y = 2x - 4.8.