To determine the intercepts of a linear equation, we use the points where the line crosses the x-axis and the y-axis. Let's understand what these intercepts represent:
1. x-intercept: This is the point where the line crosses the x-axis. At this point, the [tex]\( y \)[/tex]-coordinate is [tex]\( 0 \)[/tex]. To find the x-intercept, set [tex]\( y = 0 \)[/tex] in the linear equation and solve for [tex]\( x \)[/tex].
2. y-intercept: This is the point where the line crosses the y-axis. At this point, the [tex]\( x \)[/tex]-coordinate is [tex]\( 0 \)[/tex]. To find the y-intercept, set [tex]\( x = 0 \)[/tex] in the linear equation and solve for [tex]\( y \)[/tex].
Given the information:
- When [tex]\( y = 0 \)[/tex] she solved for [tex]\( x \)[/tex] and got [tex]\( x = -3 \)[/tex]. Therefore, the x-intercept is [tex]\( (-3, 0) \)[/tex].
- When [tex]\( x = 0 \)[/tex] she solved for [tex]\( y \)[/tex] and got [tex]\( y = 4 \)[/tex]. Therefore, the y-intercept is [tex]\( (0, 4) \)[/tex].
So, the correct statement for the intercepts is:
[tex]\( x\text{-intercept: } (-3, 0) \)[/tex]
[tex]\( y\text{-intercept: } (0, 4) \)[/tex]
These results are consistent with the definition and process of finding intercepts for a linear equation.
