Questions: Graph the line. y-4=4/3(x+2)

Transcript text: Graph the line. \[ y-4=\frac{4}{3}(x+2) \]

Solution

Solution Steps

Step 1: Rewrite the Equation in Slope-Intercept Form

The given equation is in point-slope form: \[ y - 4 = \frac{4}{3}(x + 2) \] To convert it to slope-intercept form $y = mx + b$, we solve for $y$: \[ y = \frac{4}{3}(x + 2) + 4 \] \[ y = \frac{4}{3}x + \frac{8}{3} + 4 \] \[ y = \frac{4}{3}x + \frac{8}{3} + \frac{12}{3} \] \[ y = \frac{4}{3}x + \frac{20}{3} \]

Step 2: Identify the Slope and Y-Intercept

From the slope-intercept form $y = \frac{4}{3}x + \frac{20}{3}$, we identify:

Slope ($m$) = $\frac{4}{3}$
Y-intercept ($b$) = $\frac{20}{3}$

Step 3: Determine the X-Intercept

To find the x-intercept, set $y = 0$ and solve for $x$: \[ 0 = \frac{4}{3}x + \frac{20}{3} \] \[ -\frac{20}{3} = \frac{4}{3}x \] \[ x = -\frac{20}{3} \times \frac{3}{4} \] \[ x = -5 \]

Final Answer

The line in slope-intercept form is $y = \frac{4}{3}x + \frac{20}{3}$. The slope is $\frac{4}{3}$, the y-intercept is $\frac{20}{3}$, and the x-intercept is $-5$.

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -10, "ymax": 10}, "commands": ["y = (4/3)x + (20/3)"], "latex_expressions": ["$y = \\frac{4}{3}x + \\frac{20}{3}$"]}

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