To graph the line given by the equation [tex]\(4x + 2y = 12\)[/tex], you can use the intercepts. Here is a detailed, step-by-step solution on how to find the intercepts and use them to graph the line.
### Step 1: Find the x-intercept
The x-intercept is the point where the line crosses the x-axis. To find the x-intercept, set [tex]\(y = 0\)[/tex] in the equation and solve for [tex]\(x\)[/tex].
[tex]\[
4x + 2(0) = 12
\][/tex]
[tex]\[
4x = 12
\][/tex]
[tex]\[
x = \frac{12}{4}
\][/tex]
[tex]\[
x = 3
\][/tex]
So, the x-intercept is [tex]\( (3, 0) \)[/tex].
### Step 2: Find the y-intercept
The y-intercept is the point where the line crosses the y-axis. To find the y-intercept, set [tex]\(x = 0\)[/tex] in the equation and solve for [tex]\(y\)[/tex].
[tex]\[
4(0) + 2y = 12
\][/tex]
[tex]\[
2y = 12
\][/tex]
[tex]\[
y = \frac{12}{2}
\][/tex]
[tex]\[
y = 6
\][/tex]
So, the y-intercept is [tex]\( (0, 6) \)[/tex].
### Step 3: Plot the intercepts on the coordinate plane
Now that we have the intercepts [tex]\( (3, 0) \)[/tex] and [tex]\( (0, 6) \)[/tex], we can plot these points on a coordinate plane.
- Plot the point [tex]\( (3, 0) \)[/tex] on the x-axis.
- Plot the point [tex]\( (0, 6) \)[/tex] on the y-axis.
### Step 4: Draw the line
Draw a straight line through the points [tex]\( (3, 0) \)[/tex] and [tex]\( (0, 6) \)[/tex]. This line is the graphical representation of the equation [tex]\(4x + 2y = 12\)[/tex].
By connecting these points with a straight edge, you have effectively graphed the line [tex]\(4x + 2y = 12\)[/tex] using its intercepts.
