To graph the line described by the equation [tex]\(4x + 3y = -12\)[/tex] using its intercepts, follow these steps:
### Step 1: Find the x-intercept
To find the x-intercept, set [tex]\( y = 0 \)[/tex] in the equation and solve for [tex]\( x \)[/tex].
Given equation:
[tex]\[ 4x + 3(0) = -12 \][/tex]
[tex]\[ 4x = -12 \][/tex]
[tex]\[ x = \frac{-12}{4} \][/tex]
[tex]\[ x = -3 \][/tex]
The x-intercept is at the point [tex]\((-3, 0)\)[/tex].
### Step 2: Find the y-intercept
To find the y-intercept, set [tex]\( x = 0 \)[/tex] in the equation and solve for [tex]\( y \)[/tex].
Given equation:
[tex]\[ 4(0) + 3y = -12 \][/tex]
[tex]\[ 3y = -12 \][/tex]
[tex]\[ y = \frac{-12}{3} \][/tex]
[tex]\[ y = -4 \][/tex]
The y-intercept is at the point [tex]\((0, -4)\)[/tex].
### Step 3: Plot the intercepts
On the coordinate plane, plot the x-intercept at [tex]\((-3, 0)\)[/tex] and the y-intercept at [tex]\((0, -4)\)[/tex].
### Step 4: Draw the line
Once both intercepts are plotted, draw a straight line through these two points. This line represents the equation [tex]\(4x + 3y = -12\)[/tex].
By following these steps, you can graph the line using the intercepts, and your graph will pass through the points [tex]\((-3, 0)\)[/tex] and [tex]\((0, -4)\)[/tex].
