Questions: Graph the line passing through the given point and having the indicated slope. through (1,-2) with slope -4/5 Use the graphing tool on the right to graph the line Click to enlarge graph

Graph the line passing through the given point and having the indicated slope. through (1,-2) with slope -4/5

Use the graphing tool on the right to graph the line
Click to enlarge graph

Transcript text: Graph the line passing through the given point and having the indicated slope. through $(1,-2)$ with slope $-\frac{4}{5}$ Use the graphing tool on the right to graph the line Click to enlarge graph

Solution

Solution Steps

Step 1: Determine the Equation of the Line

To find the equation of the line passing through the point $(1, -2)$ with a slope of $-\frac{4}{5}$, we use the point-slope form of a line: \[ y - y_1 = m(x - x_1) \] where $m$ is the slope and $(x_1, y_1)$ is the point. Substituting the given values: \[ y - (-2) = -\frac{4}{5}(x - 1) \] Simplifying, we get: \[ y + 2 = -\frac{4}{5}x + \frac{4}{5} \] \[ y = -\frac{4}{5}x + \frac{4}{5} - 2 \] \[ y = -\frac{4}{5}x - \frac{6}{5} \]

Final Answer

The equation of the line is: \[ y = -\frac{4}{5}x - \frac{6}{5} \]

{"axisType": 3, "coordSystem": {"xmin": -5, "xmax": 5, "ymin": -5, "ymax": 5}, "commands": ["y = (-4/5)x - (6/5)"], "latex_expressions": ["$y = -\\frac{4}{5}x - \\frac{6}{5}$"]}

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