To determine the intercepts of the line given by the equation [tex]\( y = 4x + 7 \)[/tex], we need to find both the x-intercept and the y-intercept.
### Finding the x-intercept
The x-intercept is the point where the line crosses the x-axis. At this point, the value of [tex]\( y \)[/tex] is 0.
1. Set [tex]\( y = 0 \)[/tex] in the equation [tex]\( y = 4x + 7 \)[/tex]:
[tex]\[
0 = 4x + 7
\][/tex]
2. Solve for [tex]\( x \)[/tex]:
[tex]\[
4x = -7
\][/tex]
[tex]\[
x = -\frac{7}{4}
\][/tex]
So the x-intercept is [tex]\( \left(-\frac{7}{4}, 0\right) \)[/tex].
### Finding the y-intercept
The y-intercept is the point where the line crosses the y-axis. At this point, the value of [tex]\( x \)[/tex] is 0.
1. Set [tex]\( x = 0 \)[/tex] in the equation [tex]\( y = 4x + 7 \)[/tex]:
[tex]\[
y = 4(0) + 7
\][/tex]
[tex]\[
y = 7
\][/tex]
So the y-intercept is [tex]\( (0, 7) \)[/tex].
### Final Answers
- x-intercept: [tex]\( \left(-\frac{7}{4}, 0\right) \)[/tex] which is [tex]\( (-1.75, 0) \)[/tex]
- y-intercept: [tex]\( (0, 7) \)[/tex]
