Answer:
- red: y = 5
- green: y = -2x +1
- blue: y = 2x -1
- yellow: y = -1/2x -1
Explanation:
You want the equations for the lines shown on the graph.
Slope-intercept form
The slope-intercept form of the equation for a line is ...
y = mx + b
where m is the slope, and b is the y-intercept.
Slope
The slope of a line is the ratio of its "rise" to its "run". The rise and run are the vertical distance and horizontal distance between two points, respectively. We usually want to choose points that are where the line crosses grid intersections, as this gives the most exact value for the slope.
Red line: There is no rise for any value of run. The slope is ...
m = rise/run = 0/1 = 0
Green line: The green line crosses the y-axis at y = 1, and crosses the next grid intersection to the right at (1, -1). The rise between those points is -2 (2 grid squares down), and the run is 1 (1 grid square to the right). The slope is ...
m = -2/1 = -2
Blue line: The blue line crosses the y-axis at y = -1, and crosses the next grid intersection to the right at (1, 1). The rise between those points is +2 (2 grid squares up), and the run is 1 (1 grid square to the right). The slope is ...
m = 2/1 = 2
Yellow line: The yellow line crosses the y-axis at y = -1, and crosses the next grid intersection to the right at (2, -2). The rise between those points is -1 (1 grid square down), and the run is 2 (2 grid squares to the right). The slope is ...
m = -1/2
Y-Intercept.
The y-intercept is the value of y where the line crosses the y-axis. In the slope-intercept form equation (y=mx+b), this is the value of 'b'. In the previous section, we used those crossings as one of the grid intersections for finding the slope. They are ...
- Red: +5
- Green: +1
- Blue: -1
- Yellow: -1
Equations
Using the slope and y-intercept for each line, we can now write the equations:
- Red: y = 0x +5 ⇒ y = 5
- Green: y = -2x +1
- Blue: y = 2x -1
- Yellow: y = -1/2x -1
__
Additional comment
The slope-intercept form of the equation is not the only possible way to write an equation for a line. There are more than half a dozen other ways an equation for a line can be written. Each will have its use.
Other forms include ...
ax +by = c . . . . . . . standard form
ax +by -c = 0 . . . . . general form
x/a +y/b = 1 . . . . . . . intercept form
y -k = m(x -h) . . . . . point-slope form
Intercept forms don't work well when one of the intercepts is missing. For the red line, the x-intercept is missing. Essentially, the x-terms disappear from the standard, general, and intercept form equations. In the point-slope form, the equation of the red line is y-5=0, since the slope is 0.