Finding the Equation of Straight Line Graphs - Mr-Mathematics.com - Free Printable

I will solve this problem by analyzing each of the three graphs (a, b, and c) to find their gradient (m) and y-intercept (c) in the form y = mx + c.

I'll start with graph (a).

First, look closely:
- For graph (a), I can see a straight line passing through the coordinate plane.
- The line intersects the y-axis at y = 3, so the y-intercept (c) is 3.
- To find the gradient (m), I need to calculate the change in y divided by the change in x between two points on the line. I can use the points (0, 3) and (2, 7) which appear to be on the line.
- Change in y = 7 - 3 = 4
- Change in x = 2 - 0 = 2
- Gradient m = 4/2 = 2

So for graph (a), the equation is y = 2x + 3.

Now I'll analyze graph (b).

Next, find information:
- For graph (b), I can see a straight line passing through the coordinate plane.
- The line intersects the y-axis at y = 1, so the y-intercept (c) is 1.
- To find the gradient (m), I need to calculate the change in y divided by the change in x between two points on the line. I can use the points (0, 1) and (2, 7) which appear to be on the line.
- Change in y = 7 - 1 = 6
- Change in x = 2 - 0 = 2
- Gradient m = 6/2 = 3

So for graph (b), the equation is y = 3x + 1.

Finally, I'll analyze graph (c).

Then, review the findings:
- For graph (c), I can see a straight line passing through the coordinate plane.
- The line intersects the y-axis at y = 5, so the y-intercept (c) is 5.
- To find the gradient (m), I need to calculate the change in y divided by the change in x between two points on the line. I can use the points (0, 5) and (2, 1) which appear to be on the line.
- Change in y = 1 - 5 = -4
- Change in x = 2 - 0 = 2
- Gradient m = -4/2 = -2

So for graph (c), the equation is y = -2x + 5.

I have now analyzed all three graphs and found their gradients and intercepts.

The solution is:
- Graph (a): Gradient = 2, Intercept = 3, Equation: y = 2x + 3
- Graph (b): Gradient = 3, Intercept = 1, Equation: y = 3x + 1
- Graph (c): Gradient = -2, Intercept = 5, Equation: y = -2x + 5