Question

find the equation of the line that has a slope of 2 and passes through the point (-7, -9). write the equation in point - slope form.
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the u.s. postal service charges a $18.70 flat rate for priority mail and an additional $2.40 per kilogram. write an equation in slope - intercept form where x represents the weight in kilograms of a package, and y represents its total shipping cost.
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Explanation:

Step1: Recall point - slope formula

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $m$ is the slope and $(x_1,y_1)$ is a point on the line.

Step2: Identify values of $m$, $x_1$, and $y_1$

Given $m = 2$, $x_1=-7$, and $y_1=-9$.

Step3: Substitute values into formula

$y-(-9)=2(x - (-7))$, which simplifies to $y + 9=2(x + 7)$.

Step4: Recall slope - intercept formula for cost problem

The slope - intercept form is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step5: Identify values of $m$ and $b$ for cost problem

The flat rate of $\$18.70$ is the y - intercept $b$, and the rate of $\$2.40$ per kilogram is the slope $m$.

Step6: Write the cost equation

$y = 2.4x+18.70$

Answer:

1. $y + 9=2(x + 7)$
2. $y = 2.4x+18.70$