91Ó°ÊÓ

The x-intercept of a line is the point where the line crosses the x-axis.
It occurs when the y-value is zero, meaning the point has coordinates

• ext{(x-intercept, 0)}

To find the x-intercept for the given line equation \[3x + 4y = -12\], we set \(y\) to zero and solve the equation for \(x\). Substituting \(y = 0\) into the equation yields:\[3x + 4(0) = -12\]. Simplifying gives:\[3x = -12\]. To isolate \(x\), divide both sides by 3:\[x = -4\].The line crosses the x-axis at the point \((-4, 0)\).This point is crucial as it provides one anchor point to draw the line on a coordinate plane.

The y-intercept of a line is identified as the point where the line crosses the y-axis.
This is where the x-value is zero, meaning the point has coordinates

• ext{(0, y-intercept)}

To calculate the y-intercept in the equation \[3x + 4y = -12\], we need to set \(x = 0\) and solve for \(y\). By substituting \(x = 0\) into the equation, we have:\[3(0) + 4y = -12\]. This simplifies to:\[4y = -12\]. Dividing both sides by 4, we find:\[y = -3\]. Thus, the y-intercept occurs at the point \((0, -3)\).This point allows us to identify another key coordinate on the line.

A coordinate plane is a two-dimensional space formed by two perpendicular number lines—known as the x-axis and the y-axis.
These axes intersect at a point called the origin, represented by the coordinates \((0, 0)\).The coordinate plane is divided into four sections, or quadrants.

• The first quadrant contains points where both x and y values are positive.
• The second quadrant consists of points with a negative x value and a positive y value.
• The third quadrant holds points with both x and y values negative.
• The fourth quadrant contains points with a positive x value and a negative y value.

When plotting intercepts, they provide specific locations on this plane:
The x-intercept \((-4, 0)\) is found directly on the x-axis, and the y-intercept \((0, -3)\) lies on the y-axis, making them easy to locate and use as reference points for drawing the line.

A line equation relates the coordinates of any point on a straight line.In standard form, it's often expressed as \[Ax + By = C\].This represents all the points \((x, y)\) that fall on the line formed by this equation.For the given line equation \[3x + 4y = -12\], applying the concepts of x- and y-intercepts helps us identify precise points used to graph the line.
By substituting zero for \(y\) in finding the x-intercept and zero for \(x\) in finding the y-intercept, we derive two critical points. These are essential for plotting because a line is uniquely defined by two points.Drawing a line through the plotted intercepts \((-4, 0)\) and \((0, -3)\) ensures it accurately represents the equation \[3x + 4y = -12\] on a coordinate plane.