To determine the correct statement about the second equation, we first need to find its slope and y-intercept using the given points \((-12, 20)\) and \((4, 12)\).
- Find the slope (\(m\)):
Using the formula for slope \(m = \frac{y_2 - y_1}{x_2 - x_1}\), where \((x_1, y_1) = (-12, 20)\) and \((x_2, y_2) = (4, 12)\):
\[ m = \frac{12 - 20}{4 - (-12)} = \frac{-8}{4 + 12} = \frac{-8}{16} = -\frac{1}{2} \]
- Use the slope-intercept form to find the y-intercept (\(b\)):
Using the slope \(m = -\frac{1}{2}\) and one of the points \((4, 12)\), we substitute into the equation \(y = mx + b\):
\[ 12 = -\frac{1}{2}(4) + b \ 12 = -2 + b \ b = 12 + 2 \ b = 14 \]
- Write the equation of the second line:
Now that we have the slope and y-intercept, we can write the equation of the line in slope-intercept form \(y = mx + b\):
\[ y = -\frac{1}{2}x + 14 \]
We can also rewrite it in standard form \(Ax + By = C\):
\[ \frac{1}{2}x + y = 14 \ x + 2y = 28 \quad \text{(multiply everything by 2)} \]
- Identify relationships based on the original line:
Compare this line with the first equation represented on the graph to establish if the lines intersect, parallel, or if the second line has a different slope.
- If the first equation has a slope that is different from \(-\frac{1}{2}\), the lines intersect.
- If the first equation has a slope that is equal to \(-\frac{1}{2}\), the lines are parallel.
- If the first equation has a slope that is the negative reciprocal (therefore forming perpendicular lines).
To conclude, without knowing the properties of the first line from your original question, check its slope. Once that is done, you can accurately determine which of the statements concerning points of intersection, parallelism, or perpendicularity is true regarding the second line.
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