Write an equation in slope-intercept form for the line with slope \( -\frac{1}{2} \) and \( y \)-intercept -7 . Then graph the line.
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The equation of the line in slope-intercept form (y = mx + b) with a slope of \( -\frac{1}{2} \) and a \( y \)-intercept of -7 is \( y = -\frac{1}{2}x - 7 \). This means for every 1 unit you move to the right on the x-axis, the line moves down \( \frac{1}{2} \) units on the y-axis, starting from the point (0, -7) on the y-axis. To graph this line, begin at the point (0, -7). From there, move 2 units to the right (to \( x = 2 \)), and then move 1 unit down (to \( y = -8 \)). Plot this new point at (2, -8). Continue this process to plot more points or draw the line through the points, ensuring it extends infinitely in both directions. The result will visually represent a descending line, showcasing the negative slope!
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