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 π¦ = ππ₯ + π.

02:36

### Video Transcript

Write the equation represented by the graph shown. Give your answer in the form π¦ equals ππ₯ plus π.

So we have a diagram of a straight line. And weβ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 π¦-intercept is negative four, which means that the value of π, which is the letter used here to represent the π¦-intercept, must be negative four. So I can write down the beginnings of the equation of this straight line; itβs π¦ equals ππ₯ minus four. Next, we need to find the value of π, the slope of this line. And in order to do this, I need the coordinates of two points that lie on the line.

Weβve already had identified one point, the point with coordinates zero, negative four. Looking at the graph, I can also see that thereβs a point here that would be convenient to use. This point lies on the π₯-axis and has the coordinates six, zero. So Iβ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 π¦ divided by a change in π₯. Or you can think of this as π¦ two minus π¦ one over π₯ two minus π₯ one, if you choose to label the two points as π₯ one, π¦ one and π₯ two, π¦ two. Iβm just going to look at the diagram in order to work out the change in π¦ and the change in π₯.

The change in π¦ first of all then, well that is the vertical length in this triangle. And I can see that it moves from a π¦-coordinate of negative four to a π¦-coordinate of zero. Therefore, the change in π¦ is positive four. Now, letβ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; itβs two-thirds. Finally then, I just need to substitute this value of π, the slope of the line, into the equation. So the equation of the line represented by this graph is π¦ equals two-thirds π₯ minus four.

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