Recall different forms of linear equations. Think about how you can use each of them.
Point-Slope Form: y+1= 12(x-1) Slope-Intercept Form: y= 12x- 32 Standard Form: x-2y=3 When Are They Useful? See solution.
Practice makes perfect
We are asked to write the equation of the line passing through (1,- 1) with a slope of 12 in three different forms.
Point-Slope Form
The first form we can use is the point-slope form of equations.
y-y_1=m(x-x_1)
Here, m is the slope and (x_1,y_1) is any point on the line. We are given both the slope and the coordinates of a point on the line. Hence, we can substitute m with 12 and ( x_1, y_1) with ( 1, - 1).
y-( - 1)&= 12(x- 1)
&⇓
y+1&= 12(x-1)
Slope-Intercept Form
Next, we can write the equation of the line in the slope-intercept form.
y=mx+b
In this form, m indicates the slope and b indicates the y-intercept of the line. Let's rewrite the equation that we found earlier until it matches this form.
The third form we can use to rewrite our equation is standard form.
Ax+By=C
Here, A, B, and C are real numbers and A and B cannot both be equal to 0. Let's rewrite the slope-intercept form equation into standard form.
Let's now analyze each of these forms and determine when each of them would be useful.
Form
Equation
When Is It Useful?
Point-Slope Form
y+1=1/2(x-1)
This form is useful when we have a point and a slope and we want to find an equation of a line.
Slope-Intercept Form
y=1/2x-3/2
This form is useful when we want to graph a line.
Standard Form
x-2y=3
This form is useful when we need to easily find the intercepts of the equation — particularly in real world situations. Also, it is useful for when we want to write the equation without any fractions.
