Graph Linear Equations in Slope Intercept Form - Algebra 1 Skills ... - Free Printable

I'll solve this worksheet on graphing linear equations using the slope-intercept form. Let me work through each problem systematically.

First, let me understand what's being asked. The worksheet has 12 problems where I need to either:
- Graph a given linear equation (problems 1-9), or
- Write an equation in slope-intercept form based on a given graph (problems 10-12)

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Let me start with problem 1: y = 2x + 1
- This has a slope of 2 and a y-intercept of 1.
- To graph this, I would plot the point (0, 1) on the y-axis, then use the slope (rise/run = 2/1) to find another point by going up 2 units and right 1 unit from the y-intercept.

Let me continue with the rest of the problems:

Problem 2: y = -4x - 4
- Slope = -4, y-intercept = -4
- Plot (0, -4), then go down 4 units and right 1 unit for the next point.

Problem 3: y = (1/2)x - 3
- Slope = 1/2, y-intercept = -3
- Plot (0, -3), then go up 1 unit and right 2 units for the next point.

Problem 4: y = 5x - 2
- Slope = 5, y-intercept = -2
- Plot (0, -2), then go up 5 units and right 1 unit for the next point.

Problem 5: y = 8x + 4
- Slope = 8, y-intercept = 4
- Plot (0, 4), then go up 8 units and right 1 unit for the next point.

Problem 6: y = -x + 8
- Slope = -1, y-intercept = 8
- Plot (0, 8), then go down 1 unit and right 1 unit for the next point.

Problem 7: y = 4x - 8
- Slope = 4, y-intercept = -8
- Plot (0, -8), then go up 4 units and right 1 unit for the next point.

Problem 8: y = (1/3)x
- Slope = 1/3, y-intercept = 0
- Plot (0, 0), then go up 1 unit and right 3 units for the next point.

Problem 9: y = x + 3
- Slope = 1, y-intercept = 3
- Plot (0, 3), then go up 1 unit and right 1 unit for the next point.

Now for problems 10-12, I need to write equations based on the graphs shown.

For problem 10: Looking at the graph, I can see it passes through (0, -2) and (2, 0).
- The y-intercept is -2.
- The slope is (0 - (-2))/(2 - 0) = 2/2 = 1.
- So the equation is y = x - 2.

For problem 11: Looking at the graph, I can see it passes through (0, 3) and (1, -1).
- The y-intercept is 3.
- The slope is (-1 - 3)/(1 - 0) = -4/1 = -4.
- So the equation is y = -4x + 3.

For problem 12: Looking at the graph, I can see it passes through (0, 1) and (4, 2).
- The y-intercept is 1.
- The slope is (2 - 1)/(4 - 0) = 1/4.
- So the equation is y = (1/4)x + 1.

This completes all 12 problems on the worksheet.