Question Video: Determining the Slope-Intercept Form of the Equation of a Straight-Line Graph | Nagwa Question Video: Determining the Slope-Intercept Form of the Equation of a Straight-Line Graph | Nagwa

Question Video: Determining the Slope-Intercept Form of the Equation of a Straight-Line Graph Mathematics • Third Year of Preparatory School

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Write the equation represented by the graph shown. Give your answer in the form 𝑦 = π‘šπ‘₯ + 𝑏.

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Video Transcript

Write the equation represented by the graph shown. Give your answer in the form 𝑦 equals π‘šπ‘₯ plus 𝑏.

So we have a diagram of a straight line. And we’re asked to give its equation in slope-intercept form, which means we need to work out what each of these two things are. From looking at the diagram, we can see that the 𝑦-intercept is negative four, which means that the value of 𝑏, which is the letter used here to represent the 𝑦-intercept, must be negative four. So I can write down the beginnings of the equation of this straight line; it’s 𝑦 equals π‘šπ‘₯ minus four. Next, we need to find the value of π‘š, the slope of this line. And in order to do this, I need the coordinates of two points that lie on the line.

We’ve already had identified one point, the point with coordinates zero, negative four. Looking at the graph, I can also see that there’s a point here that would be convenient to use. This point lies on the π‘₯-axis and has the coordinates six, zero. So I’m going to use these two points to calculate the slope of the line. So, the slope of the line can be calculated as a change in 𝑦 divided by a change in π‘₯. Or you can think of this as 𝑦 two minus 𝑦 one over π‘₯ two minus π‘₯ one, if you choose to label the two points as π‘₯ one, 𝑦 one and π‘₯ two, 𝑦 two. I’m just going to look at the diagram in order to work out the change in 𝑦 and the change in π‘₯.

The change in 𝑦 first of all then, well that is the vertical length in this triangle. And I can see that it moves from a 𝑦-coordinate of negative four to a 𝑦-coordinate of zero. Therefore, the change in 𝑦 is positive four. Now, let’s look at the change in π‘₯; this is the horizontal change. So I can see from the diagram that this moves from a value of zero to a value of six, which gives me a change in π‘₯ of positive six. So the slope of this line then is four over six. But this can be written as a simplified fraction; it’s two-thirds. Finally then, I just need to substitute this value of π‘š, the slope of the line, into the equation. So the equation of the line represented by this graph is 𝑦 equals two-thirds π‘₯ minus four.

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