Question

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29 write an equation in slope - intercept form for the line that passes through (-2, 5) and has a slope of -3. use of the set of axes below is optional.

Explanation:

Step1: Recall point - slope formula

The point - slope form of a linear equation is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line. We know that the line passes through the point $(-2,5)$ and has a slope $m=-3$. So we substitute $x_1=-2$, $y_1 = 5$ and $m=-3$ into the point - slope formula.
$y - 5=-3(x-(-2))$ which simplifies to $y - 5=-3(x + 2)$

Step2: Expand the right - hand side

Using the distributive property $a(b + c)=ab+ac$, we expand $-3(x + 2)$:
$y-5=-3x-6$

Step3: Solve for y (slope - intercept form)

To get the equation in slope - intercept form $y=mx + b$, we add 5 to both sides of the equation:
$y-5 + 5=-3x-6 + 5$
$y=-3x-1$

Answer:

The equation of the line in slope - intercept form is $y=-3x - 1$