Answer :
To find the [tex]$x$[/tex] and [tex]$y$[/tex] intercepts of the equation [tex]$-2x + 7y = -56$[/tex], we can follow these steps:
### Finding the [tex]\(x\)[/tex] Intercept
1. Set [tex]\(y = 0\)[/tex] in the equation: The [tex]$x$[/tex] intercept is found where the line crosses the [tex]$x$[/tex]-axis. At this point, [tex]$y = 0$[/tex].
Hence, in the equation:
[tex]\[ -2x + 7(0) = -56 \][/tex]
2. Simplify the equation:
[tex]\[ -2x = -56 \][/tex]
3. Solve for [tex]\(x\)[/tex]: Divide both sides by [tex]$-2$[/tex]:
[tex]\[ x = \frac{-56}{-2} \][/tex]
[tex]\[ x = 28 \][/tex]
Therefore, the [tex]$x$[/tex] intercept is [tex]\((28, 0)\)[/tex].
### Finding the [tex]\(y\)[/tex] Intercept
1. Set [tex]\(x = 0\)[/tex] in the equation: The [tex]$y$[/tex] intercept is found where the line crosses the [tex]$y$[/tex]-axis. At this point, [tex]$x = 0$[/tex].
Hence, in the equation:
[tex]\[ -2(0) + 7y = -56 \][/tex]
2. Simplify the equation:
[tex]\[ 7y = -56 \][/tex]
3. Solve for [tex]\(y\)[/tex]: Divide both sides by 7:
[tex]\[ y = \frac{-56}{7} \][/tex]
[tex]\[ y = -8 \][/tex]
Therefore, the [tex]$y$[/tex] intercept is [tex]\((0, -8)\)[/tex].
### Summary
The intercepts are:
- [tex]\(x\)[/tex] intercept = [tex]\((28, 0)\)[/tex]
- [tex]\(y\)[/tex] intercept = [tex]\((0, -8)\)[/tex]
These points represent where the line crosses the [tex]$x$[/tex]-axis and [tex]$y$[/tex]-axis, respectively.
### Finding the [tex]\(x\)[/tex] Intercept
1. Set [tex]\(y = 0\)[/tex] in the equation: The [tex]$x$[/tex] intercept is found where the line crosses the [tex]$x$[/tex]-axis. At this point, [tex]$y = 0$[/tex].
Hence, in the equation:
[tex]\[ -2x + 7(0) = -56 \][/tex]
2. Simplify the equation:
[tex]\[ -2x = -56 \][/tex]
3. Solve for [tex]\(x\)[/tex]: Divide both sides by [tex]$-2$[/tex]:
[tex]\[ x = \frac{-56}{-2} \][/tex]
[tex]\[ x = 28 \][/tex]
Therefore, the [tex]$x$[/tex] intercept is [tex]\((28, 0)\)[/tex].
### Finding the [tex]\(y\)[/tex] Intercept
1. Set [tex]\(x = 0\)[/tex] in the equation: The [tex]$y$[/tex] intercept is found where the line crosses the [tex]$y$[/tex]-axis. At this point, [tex]$x = 0$[/tex].
Hence, in the equation:
[tex]\[ -2(0) + 7y = -56 \][/tex]
2. Simplify the equation:
[tex]\[ 7y = -56 \][/tex]
3. Solve for [tex]\(y\)[/tex]: Divide both sides by 7:
[tex]\[ y = \frac{-56}{7} \][/tex]
[tex]\[ y = -8 \][/tex]
Therefore, the [tex]$y$[/tex] intercept is [tex]\((0, -8)\)[/tex].
### Summary
The intercepts are:
- [tex]\(x\)[/tex] intercept = [tex]\((28, 0)\)[/tex]
- [tex]\(y\)[/tex] intercept = [tex]\((0, -8)\)[/tex]
These points represent where the line crosses the [tex]$x$[/tex]-axis and [tex]$y$[/tex]-axis, respectively.
