I don't understand this and would appreciate an explanation as well :)

1 answer:

6 0

We want to solve the two equations
$e^{x}=6$
and
$4^{y+3}=3$

First equation.
Take natural log of each side.
$ln(e^{x})=ln(6)\\xln(e)=ln(6)\\
x=ln(6)=1.7918$
Note that ln(e) = 1 by definition.
Answer: x = 1.79 (nearest hundredth)

Second equation.
Take natural log of each side.
$ln(4^{y+3})=ln(3)\\
(y+3)ln(4)=ln(3)\\
y+3= \frac{ln(3)}{ln(4)} =0.7925\\y=0.7925-3=-2.2075$
Answer: y = -2.21 (nearest hundredth)

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Using the slope and the y-intercept, graph the line represented by the following equation. Then select the correct graph. 3y = 2

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First, let's write the given equation in slope-intercept form: y = mx + b

In slope-intercept form, the slope of the line is m, and the y-intercept is b. The slope is a measure of how steep the graph is at any point and is found by doing rise over run. This means the change in y values divided by the change in x values. Next, y-intercept is just where the graph crosses the y axis.

All we need to do to get the equation in slope-intercept form is to divide each term by 3. This will isolate the y.

$y= \frac{2}{3}x-2$

As you can see, the slope of the line is 2/3, and the y-intercept is -2.

To graph the line, plot a point at (0,-2). This is the point where the graph crosses the y axis. Then from that point, count up two and right 3. Plot a point here as well. Lastly, connect the two points with a straight line.

See attached picture for the graph.