1. Find an equation with slope -1/3 that contains the point (6,-4). write the equation in slope-intercept form.
2. Find the equation of a line with slope 5 containing the point (10,-5).
3. Find the equation of a line with slope 5 and y-intercept (0,4).
4. Find the equation of a line with slope -1 and y-intercept (0,-3).
(PLS PWDE PO PAKI SAGUTAN AGAD
Answer:
The given equations represent different quadratic functions in the form \(y=ax^2\), where \(a\) is the coefficient of \(x^2\).
Let's analyze each equation:
1. \(y=x^{2}\): This equation represents a quadratic function with a positive coefficient of \(x^2\). It opens upwards, forming a U-shaped graph. The vertex of the parabola is at the origin (0, 0).
2. \(y=\frac{1}{3} x^{2}\): This equation represents a quadratic function with a positive coefficient of \(x^2\), but a smaller value compared to the previous equation. It opens upwards and has a narrower shape. The vertex of the parabola is still at the origin (0, 0).
3. \(y=3 x^{2}\): This equation represents a quadratic function with a larger positive coefficient of \(x^2\) compared to the first equation. It opens upwards and has a wider shape. The vertex of the parabola is at the origin (0, 0).
4. \(y=-x^{2}\): This equation represents a quadratic function with a negative coefficient of \(x^2\). It opens downwards, forming an inverted U-shaped graph. The vertex of the parabola is at the origin (0, 0).
5. \(y=-\frac{1}{3} x^{2}\): This equation represents a quadratic function with a negative coefficient of \(x^2\), but a smaller value compared to the previous equation. It opens downwards and has a narrower shape. The vertex of the parabola is still at the origin (0, 0).
6. \(y=-3 x^{2}\): This equation represents a quadratic function with a larger negative coefficient of \(x^2\) compared to the fourth equation. It opens downwards and has a wider shape. The vertex of the parabola is at the origin (0, 0).
In summary, the correct answer option explains that the given equations represent different quadratic functions with varying coefficients of \(x^2\). It highlights the key aspects of each equation, such as the direction of opening (upwards or downwards), the shape of the graph (wide or narrow), and the position of the vertex at the origin (0, 0).