Sure! Let's find the x-intercept and y-intercept for the linear function given by the equation [tex]\( -4y = 7x + 56 \)[/tex].
### Finding the x-intercept
The x-intercept is found by setting [tex]\( y = 0 \)[/tex] in the equation of the line and solving for [tex]\( x \)[/tex].
1. Substitute [tex]\( y = 0 \)[/tex] into the equation:
[tex]\[
-4(0) = 7x + 56
\][/tex]
2. Simplify the equation:
[tex]\[
0 = 7x + 56
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
[tex]\[
7x = -56
\][/tex]
4. Divide both sides by 7:
[tex]\[
x = -8
\][/tex]
So, the x-intercept is [tex]\( x = -8 \)[/tex].
### Finding the y-intercept
The y-intercept is found by setting [tex]\( x = 0 \)[/tex] in the equation of the line and solving for [tex]\( y \)[/tex].
1. Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[
-4y = 7(0) + 56
\][/tex]
2. Simplify the equation:
[tex]\[
-4y = 56
\][/tex]
3. Solve for [tex]\( y \)[/tex]:
[tex]\[
y = \frac{56}{-4}
\][/tex]
4. Simplify:
[tex]\[
y = -14
\][/tex]
So, the y-intercept is [tex]\( y = -14 \)[/tex].
### Summary
The intercepts of the linear function [tex]\( -4y = 7x + 56 \)[/tex] are:
- x-intercept: [tex]\( x = -8 \)[/tex] (so the point is [tex]\( (-8, 0) \)[/tex])
- y-intercept: [tex]\( y = -14 \)[/tex] (so the point is [tex]\( (0, -14) \)[/tex])
