1. We are asked to find the equation of the red straight line passing approximately through points (-3,-3) and (3,5).
2. The formula for the equation of a line given two points $(x_1,y_1)$ and $(x_2,y_2)$ is:
$$y - y_1 = m(x - x_1)$$
where the slope $m$ is calculated as:
$$m = \frac{y_2 - y_1}{x_2 - x_1}$$
3. Calculate the slope $m$:
$$m = \frac{5 - (-3)}{3 - (-3)} = \frac{5 + 3}{3 + 3} = \frac{8}{6} = \frac{4}{3}$$
4. Use point-slope form with point (-3,-3):
$$y - (-3) = \frac{4}{3}(x - (-3))$$
which simplifies to:
$$y + 3 = \frac{4}{3}(x + 3)$$
5. Distribute the slope:
$$y + 3 = \frac{4}{3}x + 4$$
6. Subtract 3 from both sides to isolate $y$:
$$y = \frac{4}{3}x + 4 - 3$$
$$y = \frac{4}{3}x + 1$$
7. Therefore, the equation of the line is:
$$y = \frac{4}{3}x + 1$$
This means the line has a slope of $\frac{4}{3}$ and crosses the y-axis at 1.
This completes the solution for the first problem (c).
Line Equation C 916C2C
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