1. Find the x- and y-intercepts for the linear equations given. 2. For equation 7: \(y-4=0\) - Solve for \(y\): \(y=4\) - Equation is horizontal line. - \(x\)-intercept: none (line is parallel to x-axis, never crosses it). - \(y\)-intercept: at \(y=4\), point \((0,4)\). 3. For equation 8: \(5x + 6y = 3x + 2\) - Rearrange: \(5x - 3x + 6y = 2 \Rightarrow 2x + 6y = 2\) - Simplify: \(2x + 6y = 2\) - Find \(x\)-intercept by setting \(y=0\): \(2x=2 \Rightarrow x=1\) - Find \(y\)-intercept by setting \(x=0\): \(6y=2 \Rightarrow y = \frac{1}{3}\) 4. For equation 9: \(\frac{1}{2} y^2 = 1\) - Multiply both sides by 2: \(y^2 = 2\) - Take square root: \(y = \pm \sqrt{2}\) - This is not a linear equation with an x-intercept in traditional sense; no \(x\)-intercept given. 5. For graphs 10, 11 and 12, they are lines through origin: - Graph 10: Line with positive slope through origin, passes \( (0,0) \), so intercepts are \(x=0, y=0\). - Graph 11 and 12: Lines with negative slope passing through origin, intercepts also at \( (0,0) \). 6. For equation 13: \(y=4\) - Horizontal line crossing y-axis at 4. - \(x\)-intercept: none. - \(y\)-intercept: \((0,4)\) 7. For equation 14: \(y=3x\) - Passes through origin. - \(x\)-intercept: \((0,0)\) - \(y\)-intercept: \((0,0)\) 8. For equation 15: \(y=x+4\) - \(y\)-intercept: \((0,4)\) - \(x\)-intercept: set \(y=0\), \(0=x+4 \Rightarrow x=-4\), so \((-4,0)\) 9. For equation x - y = 3 - Find \(x\)-intercept \((y=0)\): \(x=3\) - Find \(y\)-intercept \((x=0)\): \(-y=3 \Rightarrow y=-3\) 10. For equation 17: \(10x = -5y\) - Rearrange to \(10x + 5y=0\) - \(x\)-intercept \((y=0)\): \(10x=0 \Rightarrow x=0\) - \(y\)-intercept \((x=0)\): \(5y=0 \Rightarrow y=0\) 11. For equation 18: \(4x = 2y + 6\) - Rearrange: \(4x - 2y = 6\) - \(x\)-intercept \((y=0)\): \(4x=6 \Rightarrow x= \frac{3}{2}\) - \(y\)-intercept \((x=0)\): \(-2y=6 \Rightarrow y=-3\) Final answers summarized: -7: x-intercept none, y-intercept (0,4) -8: x-intercept (1,0), y-intercept (0,1/3) -9: No x-intercept (nonlinear), y = \(\pm \sqrt{2}\) -10: x=0,y=0 -11: x=0,y=0 -12: x=0,y=0 -13: x intercept none, y-intercept (0,4) -14: x intercept (0,0), y-intercept (0,0) -15: x intercept (-4,0), y-intercept (0,4) - x - y=3: x intercept (3,0), y intercept (0,-3) -17: x intercept (0,0), y intercept (0,0) -18: x intercept (3/2,0), y intercept (0,-3)