Using the graph, derive the equation of the line in slope-intercept form.

Question

1,3 and 0.-2

Answer 1

To find the equation of the line in slope-intercept form, we need to first find the slope of the line. The slope is given by the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (1, 3) and (x2, y2) = (0, -2)

m = (-2 - 3) / (0 - 1) = (-5) / -1 = 5

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. The point-slope form is:

y - y1 = m(x - x1)

Using the point (1, 3):

y - 3 = 5(x - 1)

Now, we can simplify this to slope-intercept form by expanding:

y - 3 = 5x - 5
y = 5x - 5 + 3
y = 5x - 2

Therefore, the equation of the line in slope-intercept form is y = 5x - 2.