Question

Use the graph to derive the equation of the line in slope-intercept form.

(1 point)

coordinates on graph: (1,3) (0, -2)

Answer 1

To find the slope of the line, we will use the formula for slope:

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

Substitute the coordinates (1,3) and (0, -2) into the formula:

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

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Choose one of the points (1,3) to substitute as (x1, y1):

y - 3 = 5(x - 1)

Now, simplify the equation:

y - 3 = 5x - 5

To write the equation in slope-intercept form (y = mx + b), isolate y:

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

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