Answer:
To determine the coordinates of the intercepts with the axes, we need to find the points where a graph intersects the x-axis (x-intercept) and the y-axis (y-intercept).
X-Intercept:
To find the x-intercept, we set y = 0 and solve for x. This means we are looking for the point(s) where the graph crosses the x-axis.
Y-Intercept:
To find the y-intercept, we set x = 0 and solve for y. This means we are looking for the point(s) where the graph crosses the y-axis.
Let's work through an example to illustrate this process:
Suppose we have an equation of a line: y = 2x + 3.
X-Intercept:
Setting y = 0:
0 = 2x + 3
2x = -3
x = -3/2
The x-intercept is (-3/2, 0).
Y-Intercept:
Setting x = 0:
y = 2(0) + 3
y = 3
The y-intercept is (0, 3).
Therefore, for the equation y = 2x + 3, the intercepts with the axes are (-3/2, 0) for the x-intercept and (0, 3) for the y-intercept.