# Video: Graphing Functions

Which of the following is the function represented by the shown graph? [A] π¦ = (3/2)π₯ + 2 [B] π¦ = 2π₯ + (2/3) [C] π¦ = (2/3)π₯ β 2 [D] π₯ = (2/3)π¦ + 2 [E] π¦ = (2/3)π₯ + 2

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### Video Transcript

Which of the following is the function represented by the shown graph? Option A, π¦ equals three-halves π₯ plus two. Option B, π¦ equals two π₯ plus two-thirds. Option C, π¦ equals two-thirds π₯ minus two. Option D, π₯ equals two-thirds π¦ plus two. Or option E, π¦ equals two-thirds π₯ plus two.

Letβs recall that the general form of a linear equation is π¦ equals ππ₯ plus π or π¦ equals ππ₯ plus π, where the constant term of π or π represents the π¦-intercept of the function. The value of π will indicate the slope or gradient of the line. So therefore, if we were to calculate the slope and the π¦-intercept of this drawn function, we could work out what the function is. We can recall that, between two coordinates π₯ one, π¦ one and π₯ two, π¦ two, the slope is equal to π¦ two minus π¦ one over π₯ two minus π₯ one.

We can select any two coordinates on the line for π₯ one, π¦ one and π₯ two, π¦ two. But often the easiest ones to pick are those which have integer values. We can see here that zero, two and three, four both lie on the line. It doesnβt matter which coordinate we designate as π₯ one, π¦ one and which we designate as π₯ two, π¦ two. To find the slope, we substitute in our π¦ two and π¦ one values to give us four minus two over the π₯ two minus π₯ one values, which is three minus zero. Simplifying this, we have a slope of two-thirds.

To find the π¦-intercept, we look at the graph to see where it crosses the π¦-axis. And that happens when the π¦-value is two. We can then fill in our values of slope and π¦-intercept into the general equation. We found that the slope π is equal to two-thirds and the π¦-intercept of π is equal to two. And so our answer is that given in option E, π¦ equals two-thirds π₯ plus two.