How do you graph the function y=-2/3x+4?

1 Answer
Jan 23, 2017

There are several strategies you can use to approach this, but since the given equation is in slope-intercept form, let's take advantage of that.

When the equation of a line is given in the form of
y = color(purple)(m)x + color(blue)(b), then

color(purple)(m) = the slope of the line (color(purple)(m)=(Delta y)/(Delta x)) and
color(blue)(b) = the y-intercept or where the line crosses the y-axis

Since we know that color(blue)(b) = 4, we know the line crosses the y-axis at y=4. In other words, the line passes through the point (0,4).

Then, applying the slope to that point, we can find a second point on the line.

color(purple)(m) = (Delta y)/(Delta x) = -2/3 = (-2)/3 = 2/-3

This tells us that when x changes by 3 units (Delta x), y changes by -2 units (Delta y)

Starting at (0,4), we can apply the slope:

Delta x = 3 = x_2 - 0 => x_2 = 3
Delta y = -2 = y_2 - 4 => y_2 = 2

The point (3,2) will be on the line. Plotting these two points (0,4) and (3,2) and drawing a straight line through these points will give you the graph of the function y=-2/3+4