Sure! Let's analyze each of the given linear equations and match them with their respective forms.
1. Equation: [tex]\( y + 6 = -3(x - 1) \)[/tex]
- This equation follows the point-slope form, which is given by the formula [tex]\( y - y_1 = m(x - x_1) \)[/tex]. In this form:
- [tex]\( y_1 \)[/tex] is the y-coordinate of a point on the line.
- [tex]\( x_1 \)[/tex] is the x-coordinate of a point on the line.
- [tex]\( m \)[/tex] is the slope of the line.
- By comparing [tex]\( y + 6 = -3(x - 1) \)[/tex] with [tex]\( y - y_1 = m(x - x_1) \)[/tex], we can see that it matches the point-slope form.
2. Equation: [tex]\( 2x - 5y = 9 \)[/tex]
- This equation follows the standard form, which is given by the formula [tex]\( Ax + By = C \)[/tex]. In this form:
- [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( C \)[/tex] are constants.
- By inspecting [tex]\( 2x - 5y = 9 \)[/tex], it is clear that it fits the standard form criterion.
3. Equation: [tex]\( y = -x + 8 \)[/tex]
- This equation follows the slope-intercept form, which is given by the formula [tex]\( y = mx + b \)[/tex]. In this form:
- [tex]\( m \)[/tex] is the slope of the line.
- [tex]\( b \)[/tex] is the y-intercept.
- By comparing [tex]\( y = -x + 8 \)[/tex] with [tex]\( y = mx + b \)[/tex], we can see that it matches the slope-intercept form.
### Summary:
- [tex]\( y + 6 = -3(x - 1) \)[/tex] is in point-slope form.
- [tex]\( 2x - 5y = 9 \)[/tex] is in standard form.
- [tex]\( y = -x + 8 \)[/tex] is in slope-intercept form.
These are the correct matches for each form of the linear equations given.
