Pay close attention to the features of the forms of a linear equation.
See solution.
Practice makes perfect
We will recall the three forms of writing a linear equation and determine when it is more useful to use each of them.
Slope-Intercept Form
Let's look at the slope-intercept form.
y= mx + b
Here m is the slope of the line and b is the y-intercept. This form is useful when it is easy to identify the slope and the y-intercept in the graph. Recall that the y-intercept is the value of y at which the line intercepts the y-axis.
Point-Slope Form
Let's now consider the point-slope form.
y-y_1= m(x-x_1)
Here, m is the slope of the line and (x_1,y_1) is a known point. If we can calculate the slope by identifying two points, we can use this form. It does not matter if we cannot identify the y-intercept precisely.
Standard form
Let's finally look at the standard form.
Ax + By = C
Here A, B, and C are real numbers, and A and B are not zero. Although these constants are harder to read from a graph, having the equation in standard form has its advantages. The most important advantage of this form is that we can easily calculate the intercepts. We can find the x-intercept by substituting y= 0.
