Answer:
[tex]y=2x+3[/tex]
Step-by-step explanation:
1. Approach
Slope intercept form is a way of expressing an equation of a line using the slope of a line, and its y-intercept. The general format for the equation of a line in slope-intercept form is the following,
[tex]y=mx+b[/tex]
Find each of the missing pieces of information and substitute it into the equation to find the equation of the line.
2. Find the slope
The slope of a line is the change in the line is can be found using the following formula,
[tex]\frac{y_2-y_2}{x_2-x_1}[/tex]
As one can see on the given graph, two points on the line are the following,
[tex](-2, -1), (-1, 1)[/tex]
Substitute the points into the formula and solve for the slope,
[tex]\frac{(1)-(-1)}{(-1)-(-2)}[/tex]
[tex]=\frac{2}{1}\\\\=2[/tex]
3. Find the y-intercept
The y-intercept of a line is where the line intersects the y-axis. As one can see this point is the following,
[tex](0,3)[/tex]
Thus the y-intercept is (3).
4. Put the information together
Putting all of this information together, substitute the found information into the general equation for slope-intercept form. One can see that the equation of a line is the following,
[tex]y=2x+3[/tex]
