Write the equation of the line in slope-intercept form.

Question

x/-2/2/10
y/1/2/4

Answer 1

To find the equation of the line, we first need to find the slope (m) and the y-intercept (b) from the given points (x1, y1) and (x2, y2).

Given points: (2, 1) and (10, 4)

Slope (m) = (y2 - y1) / (x2 - x1)
Slope (m) = (4 - 1) / (10 - 2)
Slope (m) = 3 / 8

Now, we have the slope (m) = 3/8. To find the y-intercept (b), we need to pick a point on the line. Let's pick point (2, 1).

Using the slope-intercept form of a line (y = mx + b), we substitute the values of m and the point (2, 1) into the equation to solve for the y-intercept.

1 = (3/8) * 2 + b
1 = 3/4 + b
b = 1 - 3/4
b = 1/4

Now, we have the slope (m) = 3/8 and the y-intercept (b) = 1/4.

The equation of the line in slope-intercept form is:
y = (3/8)x + 1/4