Q1: For each linear equation, identify the slope \( (m) \) and the \( v \)-intercept ( \( b \) ) a. \( y=4 x-5 \) b. \( y=11+\frac{2}{3} x \) C. \( y=\frac{2}{3}-x \) d. \( 6-\frac{9}{2} x=y \) \begin{tabular}{lll|}\( \begin{array}{ll}\text { Q2) Write the equation of a line using } y=m x+b \\ \text { a) Slope }=5, y \text {-intercept }=3 & \text { b) Slope }=-1, y \text {-intercept }=-6\end{array} \)\end{tabular}

For the given linear equations, the slope \( (m) \) and the \( y \)-intercept \( (b) \) are as follows: a. The slope \( m = 4 \) and the \( y \)-intercept \( b = -5 \). b. The slope \( m = \frac{2}{3} \) and the \( y \)-intercept \( b = 11 \). c. The slope \( m = -1 \) and the \( y \)-intercept \( b = \frac{2}{3} \). d. Rearranging gives \( y = -\frac{9}{2}x + 6 \), so the slope \( m = -\frac{9}{2} \) and \( b = 6 \). Now, writing the equations of lines: a. \( y = 5x + 3 \) b. \( y = -1x - 6 \) or simply \( y = -x - 6 \) Understanding slopes and intercepts can feel like cracking a code! The slope tells you how steep the line is, while the \( y \)-intercept represents where your line crosses the \( y \)-axis. If the slope is positive, you’re climbing up; if it’s negative, get ready for a downhill ride! In the real world, lines and their equations help in creating graphs for data analysis, predicting trends, and even in engineering! Imagine plotting your savings over time or tracking how fast you can run on a chart—linear equations are the backbone of these visual stories. Embrace them to better understand relationships in daily life!