91Ó°ÊÓ

The x-intercept is the point where a graph crosses the x-axis. To find this point for the equation \[ 4x + y = 4 \], we set y to 0 and then solve for x. This is because any point on the x-axis has a y-coordinate of 0. So, we replace y with 0 in the equation:
\[ 4x + 0 = 4 \] which simplifies to \[ 4x = 4 \] then divide both sides by 4:
\[ x = 1 \] Therefore, the x-intercept is (1, 0). This means the graph of the equation crosses the x-axis at the point (1, 0). Finding the x-intercept helps in graphing because it gives us a clear point through which the line passes.

The y-intercept is the point where a graph crosses the y-axis. To find this point for the equation \[ 4x + y = 4 \], we set x to 0 and then solve for y. This is because any point on the y-axis has an x-coordinate of 0. So, we replace x with 0 in the equation:
\[ 4(0) + y = 4 \] which simplifies to:
\[ y = 4 \] Therefore, the y-intercept is (0, 4). This means the graph of the equation crosses the y-axis at the point (0, 4). Finding the y-intercept provides another clear point for drawing the line.

The coordinate plane is a two-dimensional surface on which we can plot points, lines, and curves. It's defined by two perpendicular axes: the horizontal x-axis and the vertical y-axis that intersect at a point called the origin, labeled as (0,0). Each point on the coordinate plane is represented by an ordered pair (x, y).
To graph a linear equation like \[ 4x + y = 4 \] on the coordinate plane, we first identify two key points: the x-intercept and the y-intercept. For this equation, we have already found that the x-intercept is (1, 0) and the y-intercept is (0, 4). Next, we plot these points on the coordinate plane.

• Place a point at (1, 0)
• Place another point at (0, 4)

Finally, draw a straight line through these two points, extending it in both directions. This line represents all the solutions of the equation \[ 4x + y = 4 \]. The coordinate plane visually illustrates these solutions, making it a powerful tool in algebra.