Study case: finding the equation of a straight line In this Year 9 Straight Line Graphs Problem Tutor, I use one study case to connect coordinate work with algebra. The problem is: find the equation of the line with gradient 3 that passes through the point (0, 2). The answer is y = 3x + 2. I like this example because it introduces the structure y = mx + c in a simple and memorable way. Before solving, I ask the student what m and c mean in y = mx + c. The m is the gradient, which tells us how steep the line is. The c is the y-intercept, which tells us where the line crosses the y-axis. If a line passes through (0, 2), it crosses the y-axis at 2, so c = 2. The gradient is given as 3, so m = 3. Therefore the equation is y = 3x + 2. Method 1 is the direct y = mx + c method. We substitute m = 3 and c = 2 into y = mx + c. This gives y = 3x + 2. I explain that this method is quick because the point given is already on the y-axis. When x = 0, the y-value is the intercept. Method 2 is the table method. If y = 3x + 2, then when x = 0, y = 2. When x = 1, y = 5. When x = 2, y = 8. The y-values increase by 3 each time x increases by 1, so the gradient is 3. This method helps the student check that the equation matches the given gradient and starting point. Method 3 is the graph method. I plot the point (0, 2). A gradient of 3 means rise 3 for every run 1. From (0, 2), I can move right 1 and up 3 to reach (1, 5), then again to reach (2, 8). Drawing through these points gives the line y = 3x + 2. This visual route helps students understand gradient as movement on a grid. After the methods, I compare them. The algebra method is fastest. The table method checks the pattern. The graph method builds visual understanding. I want students to use all three because straight-line graphs appear in KS3, GCSE algebra, coordinate geometry and real-life graph interpretation. Common mistakes include swapping gradient and intercept, writing y = 2x + 3, forgetting that the y-intercept happens when x = 0, and drawing a line with the wrong steepness. I use these mistakes to guide explanation. If a student confuses m and c, I return to the graph and show where each value appears. This topic is important because y = mx + c is one of the most useful forms in school algebra. It connects sequences, proportional reasoning, graph drawing and coordinate geometry. A student who understands gradient and intercept in Year 9 will be better prepared for GCSE graph questions. A useful extension is to find the equation of a line with gradient -2 passing through (0, 5). Another extension is to find the equation from two points, where the gradient must be calculated first. These extensions build towards higher GCSE straight-line graph skills. In one-to-one tutoring, I would finish by asking the student to draw three lines with different gradients and intercepts, then describe what changed. This builds fluency and helps the student see equations as pictures, not just symbols. For support with this topic, students can book one-to-one tutor services: https://www.mastermathstutoring.co.uk/services. For the wider course page, visit KS3 Maths tutoring: https://www.mastermathstutoring.co.uk/ks3. To ask about lessons or availability, use contact MasterMaths Tutoring: https://www.mastermathstutoring.co.uk/contact-me.