a Begin by determining two points on the line and finding the slope.
B
b Can you identify the y-intercept of the line?
A
aPoint-Slope Form: y-3=2(x-0)
Slope-Intercept Form: y=2x+3 Standard Form: -2x+y=3
B
bEquation: Slope-intercept form
Explanation: See solution
Practice makes perfect
a We will first write an equation in point-slope form. Therefore, we should first indicate two points on the line and find its slope by the Slope Formula.
Now that we indicated the points, we can apply the formula.
Since we know the slope and at least one point that the line passes through, we can write its equation. Let the point (0,3) be our reference point.
&Point-Slope Form &&Line Equation
&(y-y_1)=m(x-x_1) &&(y-3)=2(x- )
The line equation can also be written in slope-intercept form. Looking at the graph, we see that the line crosses the y-axis at the point (0,3). This is the y-intercept. Let's use this point and the slope to write the equation.
&Slope-Intercept Form &&Line Equation
&y=mx+b &&y=2x+3
Finally, there is a third way to write a line equation called standard form. To write the equation in this form, we will gather the variable terms in the equation that is in slope-intercept form on the left-hand side.
&Standard Form &&Line Equation
& Ax+ By= C && -2x+ 1y= 3
b Since the line crosses the y-axis at the point (0,3), we can immediately identify its y-intercept b. We can also determine a second point on it to find its slope m. Combining the slope and the y-intercept we can say that slope-intercept equation is the easiest to write.
