Find the axis intercepts of a line

Which point is the y-intercept?

Predict the change before calculating both crossings. If a changes from 1 to 3, what happens to the x-intercept coordinate?

Equation

\(\displaystyle ax+4y=24\)

Coefficient values

\(\displaystyle a=1,\quad a=3\)

Compare both axis crossings as the coefficient changes from one to three

When the coefficient changed from one to three, what happened to the intercept coordinates?

Find the axis crossings

An axis intercept is a point shared by the line and an axis. On each axis, one coordinate is zero. Substitute that coordinate and solve for the other one

1. 1The horizontal-axis crossing Set the vertical coordinate to zero. Divide by the coefficient of the horizontal variable \(\displaystyle \begin{aligned}y&=0\\3x+7(0)&=42\\3x&=42\\x&=14\\I_x&=(14,0)\end{aligned}\)
2. 2The vertical-axis crossing Set the horizontal coordinate to zero. Divide by the coefficient of the vertical variable \(\displaystyle \begin{aligned}x&=0\\3(0)+7y&=42\\7y&=42\\y&=6\\I_y&=(0,6)\end{aligned}\)
3. 3Sketch through two different points Plot the two crossings, then draw a straight line through them and extend it in both directions. If both intercepts are the origin, they give only one point. Use the equation to find another point

Find the x-coordinate of the x-intercept

Points on the horizontal axis have zero vertical coordinate

Find the y-coordinate of the y-intercept

Points on the vertical axis have zero horizontal coordinate. Keep the sign of the remaining coefficient

Which operation is the first error in this attempt to find the y-intercept?

Which ordered pair of intercept points matches the graph?

Find the x-coordinate of the horizontal-axis crossing

Which two crossings would you use to sketch this line?

The x-intercept is (−4,0). Find k.

Both intercepts of this line are (0,0). Which action gives enough information to sketch it?

Which statement about the line y=−3 is correct?

Which statement about the line x=2 is correct?

Crossing, no crossing, or an entire axis

Two distinct crossings are a useful shortcut for oblique lines. Special lines need a direct coordinate check

1. 1Through the origin Both intercepts can name the same point. Find another distinct point before drawing
2. 2Horizontal or vertical A line away from the origin misses its parallel axis. Use two points with the required fixed coordinate
3. 3Coinciding with an axis When the line is the horizontal axis, every point on that axis is on the line. When the line is the vertical axis, every point on that axis is on the line. There is no unique crossing with the coincident axis