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Determine the y-intercept from a graph

The y-intercept of a linear relation is the point where its graph crosses the y-axis, so its x-coordinate is always 0; the intercept may be positive, negative, or zero. Learners read the corresponding y-value using the graph’s scale and connect it to the constant term bb in y=mx+by=mx+b, distinguishing it from the x-intercept and interpreting it as the output when the input is zero.

Detailed Explanation: Determine the y-intercept from a graph

The yy-intercept is where a graph crosses the yy-axis. Since every point on the yy-axis has an xx-coordinate of 00, the yy-intercept always has the form

(0,b).(0,b).

The value bb is also the constant term in the equation

y=mx+b.y=mx+b.

Example: A line crosses the yy-axis at the horizontal grid line labeled 44. It crosses the xx-axis at 88.

  1. Find the yy-axis. It is the vertical axis.

  2. Find where the line crosses that axis.

  3. Read the yy-value using the scale. The line crosses at (y=4)(y=4).

  4. Write the intercept as an ordered pair:

(0,4) (0,4)

Therefore, the yy-intercept is ((0,4))((0,4)). This means that when the input (x=0)(x=0), the output is (y=4)(y=4). In an equation such as

y=12x+4,y=-\frac{1}{2}x+4,

the 44 is the constant term bb.

Do not use the point ((8,0))((8,0)), because that is where the graph crosses the xx-axis, not the yy-axis.

Learn by doing: Determine the y-intercept from a graph

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