Graphing linear equations unit test
Use the graph to derive the equation of the line in slope-intercept form (1/point)
To determine the equation of the line in slope-intercept form from the graph, we need to find the slope and the y-intercept of the line.
1. Identify two points on the line: Let's choose two points on the line. For example, we can choose the point (2, 4) and (5, 8).
2. Calculate the slope:
Slope (m) = (y2 - y1) / (x2 - x1)
Slope (m) = (8 - 4) / (5 - 2)
Slope (m) = 4 / 3
Slope (m) = 4/3
3. Calculate the y-intercept:
Now we can substitute one of the points into the slope-intercept form equation y = mx + b to solve for the y-intercept (b).
Let's use point (2, 4):
4 = 4/3(2) + b
4 = 8/3 + b
b = 4 - 8/3
b = 12/3 - 8/3
b = 4/3
4. Write the equation of the line in slope-intercept form:
Now, we have the slope (m) = 4/3 and y-intercept (b) = 4/3, so the equation of the line in slope-intercept form is:
y = 4/3x + 4/3