Question

use the graph to derive the equation for the line in slope-intercept form.

Answer 1

To derive the equation for the line in slope-intercept form, we need to first identify the slope of the line and the y-intercept.

From the given graph, we can see that the line passes through the point (0, 3) and (3, 6).

The slope of the line can be calculated as:
m = (y2 - y1) / (x2 - x1)
m = (6 - 3) / (3 - 0)
m = 3 / 3
m = 1

Now that we have the slope, we can use the point-slope form of the equation of a line to find the equation in slope-intercept form.

y - y1 = m(x - x1)
y - 3 = 1(x - 0)
y - 3 = x

Now we can simplify it to slope-intercept form:
y = x + 3

Therefore, the equation of the line in slope-intercept form is y = x + 3.